Algebra and Trigonometry (6th Edition)

Chapter 5

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; overestimates the amount in the figure by ; ... more

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A graph of a function along with four secant ... more

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Construct a table of values for the function.... more

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Sketch the graph of the function . ; The ... more

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Sketch the graph of the function . ; The ... more

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; Identify the number of years that have lapsed ... more

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; Functions of the form , with taken to be an ... more

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; Given an exponential function with positive ... more

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; Construct a table of values for increasing ... more

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; Interest is accumulated and is added to the ... more

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semiannually ; Interest is accumulated two times, ... more

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; Input the expression on a scientific or ... more

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; Input the expression on a scientific or ... more

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; Input the expression on a scientific or ... more

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; Input the expression on a scientific or ... more

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; Input the expression on a scientific or ... more

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; Input the expression on a scientific or ... more

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; Input the expression on a scientific or ... more

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; Input the expression on a scientific or ... more

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; Input the expression on a scientific or ... more

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; Input the expression on a scientific or ... more

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Construct a table of values for the function.Take ... more

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Construct a table of values for the function.Take ... more

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Construct a table of values for the function.Take ... more

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Construct a table of values for the function.Take ... more

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Construct a table of values for the function.Take ... more

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Construct a table of values for the function.Take ... more

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Construct a table of values for the function.Take ... more

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Construct a table of values for the function.Take ... more

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The point on the given figure is not on the graph... more

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The points and on the given figure are not on ... more

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The point on the given figure is not on the graph... more

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The point on the given figure is also on the ... more

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The points and on the given figure are not on ... more

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The point on the given figure is not on the graph... more

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Horizontal Asymptote: Domain: Range: ; Sketch the ... more

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Horizontal Asymptote: Domain: Range: ; Sketch the ... more

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Horizontal Asymptote: Domain: Range: ; Sketch the ... more

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Horizontal Asymptote: Domain: Range: ; Sketch the ... more

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Horizontal Asymptote: Domain: Range: ; Sketch the ... more

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Horizontal Asymptote: Domain: Range: ; Sketch the ... more

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Horizontal Asymptote: Domain: Range: ; Sketch the ... more

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Horizontal Asymptote: Domain: Range: ; Sketch the ... more

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Horizontal Asymptote: Domain: Range: ; Sketch the ... more

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Horizontal Asymptote: Domain: Range: ; Sketch the ... more

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Horizontal asymptote: Domain: Range: ; The graph ... more

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Horizontal asymptote: Domain: Range: ; The graph ... more

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Horizontal asymptote: Domain: Range: ; The graph ... more

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Horizontal asymptote: Domain: Range: ; The graph ... more

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Horizontal asymptote: Domain: Range: ; The graph ... more

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Horizontal asymptote: Domain: Range: ; The graph ... more

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Horizontal asymptote: Domain: Range: ; The graph ... more

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Horizontal asymptote: Domain: Range: ; The graph ... more

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Horizontal asymptote: Domain: Range: ; Since is ... more

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Horizontal asymptote: Domain: Range: ; Since is ... more

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Horizontal asymptote: Domain: Range: ; The graph ... more

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Horizontal asymptote: Domain: Range: ; The graph ... more

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Horizontal Asymptote/s: ; Sketch the graph of the ... more

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Horizontal Asymptote/s: ; Sketch the graph of the ... more

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Horizontal Asymptote/s: ; Sketch the graph of the ... more

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Horizontal Asymptote/s: ; Sketch the graph of the ... more

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Horizontal Asymptote/s: and ; Sketch the graph of... more

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Horizontal Asymptote/s: and ; Sketch the graph of... more

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Investment at compounded monthly ; For investment... more

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Investment at compounded quarterly ; For ... more

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; Graph both functions on a single Cartesian ... more

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; Graph both functions on a single Cartesian ... more

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Construct tables of values for the two equations ... more

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Construct tables of values for the two equations ... more

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; Observing some of the given ordered pairs on ... more

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; Observing some of the given ordered pairs on ... more

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; Observing some of the given ordered pairs on ... more

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; Observing some of the given ordered pairs on ... more

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; unsafe for human habitation ; Identify the ... more

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; Given , , and , plug these values into the ... more

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; Given , , and years, plug these values into ... more

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As the exponent gets closer to , the closer the ... more

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As the exponent gets closer to ,  the closer the ... more

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The second model ; Identify the number of years ... more

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The second model ; Identify the number of years ... more

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An exponential function with base is a function ... more

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The natural exponential function is the ... more

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The expression gets closer to . ; Evaluate the ... more

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Since , locate the -value corresponding to on the... more

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The statement does not make sense. ; Graph the ... more

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The statement makes sense. ; Initially, an image ... more

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The statement does not make sense. ; Based on the ... more

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The statement makes sense. ; The balance, or ... more

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The statement is false. Correct Statement: “As the... more

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The statement is false. Correct Statement: “The ... more

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The statement is false. Correct Statement: “If , ... more

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The statement is true. ; Applying properties of ... more

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(a) (b) (c) (d) ; Since graphs (a) and (b) are at ... more

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Construct a table of values for the function over ... more

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; Add on both sides of the equation.Apply the ... more

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, , and ; Calculate all factors of the constant ... more

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Solution set: ; Isolate zero on one side of the ... more

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It is difficult to solve for in the equation . ; ... more

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; is the square of . ; By a law of exponents, .... more

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; Zero is already isolated on one side of the ... more

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Set up a table of coordinates for . ;   ; ... more

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; Find for . ; more

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; Substitute into .  ; more

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The magnitude is . ; Substitute in the function... more

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; very well ; Substitute into .  The given figure... more

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; In the given logarithmic equation, is the base... more

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logarithmic ; The given function is a logarithmic ... more

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; In the given equation, the base and answer are ... more

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; In the given equation, the base is , the answer... more

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; Use inverse properties of logarithms.  ; more

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; Use inverse properties of logarithms.  ; more

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; The domain of a function is the set of input ... more

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- axis ; The domain of the function consists of ... more

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units up ; The function is shifted units up from... more

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units left ; The is shifted units left of since... more

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-axis ; The is reflected about the -axis with ... more

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-axis ; The is reflected about the -axis with ... more

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; To find the domain of the given function, ... more

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common ; The common logarithmic function is ... more

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natural ; The natural logarithmic function is ... more

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; Remember that logs are exponents. If 4 is the ... more

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; Remember that logs are exponents. If 6 is the ... more

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; Remember that logs are exponents. If 2 is the ... more

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; Remember that logs are exponents. If 2 is the ... more

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; Remember that logs are exponents. If 5 is the ... more

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; Remember that logs are exponents. If 3 is the ... more

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; Remember that logs are exponents. If is the ... more

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; Remember that logs are exponents. If is the ... more

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; In the expression , the exponent is 3 and the ... more

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; In the expression , the exponent is 4 and the ... more

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; In the expression , the exponent is and the ... more

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; In the expression , the exponent is and the ... more

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; Start by recognizing that is the same as . In ... more

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; Start by recognizing that is the same as . In ... more

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; In the expression , the exponent is 2 and the ... more

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; 15 is the base and 2 is the exponent.means... more

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; is the base and 3 is the exponent.means . ; more

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; is the base and 3 is the exponent.means . ; more

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; By the definition of logarithmic function, is ... more

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; 8 is the base and is the exponent.means . ; more

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2 ; Express 16 as a power of 4. ; Since 2 is the ... more

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2 ; Express 49 as a power of 7. ; Since 2 is the ... more

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6 ; Express 64 as a power of 2. ; Since 6 is the ... more

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3 ; Express 27 as a power of 3. ; Since 3 is the ... more

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; Express as a power of 5. ; Since is the ... more

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; Express as a power of 6. ; Since is the ... more

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; Express as a power of 2. ; Since is the ... more

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; Express as a power of 3. ; Since is the ... more

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; Express as a power of 7. ; Since is the ... more

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; Express as a power of 6. ; Since is the ... more

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; Use the general logarithmic formulas,   and... more

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; Express as a power of 3. ; Since is the ... more

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; Express 8 as a power of 64. ; Since is the ... more

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; Express 9 as a power of 81. ; Since is the ... more

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1 ; Express 5 as a power of 5. ; Since 1 is the ... more

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1 ; Express 11 as a power of 11. ; Since 1 is the ... more

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0 ; Express 1 as a power of 4. ; Since 0 is the ... more

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0 ; Use the property that . The property works ... more

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7 ; Use the property that  The property works ... more

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6 ; Use the property that . The property works ... more

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19 ; Use the property that . The property works ... more

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23 ; Use the property that . The property works ... more

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Find the values of at . Then write the ... more

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Find the values of at . Then write the ... more

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Find the values of at . Then write the ... more

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Find the values of at . Then write the ... more

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The graph of passes through the point (because... more

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The graph of passes through the point (because... more

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The graph of passes through the point (because... more

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The graph of passes through the point (because... more

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The graph of passes through the point (because... more

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The graph of passes through the point (because... more

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Vertical asymptote: Domain: Range: ; Use key ... more

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Vertical asymptote: Domain: Range: ; Use key ... more

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Vertical asymptote: Domain: Range: ; Use key ... more

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Vertical asymptote: Domain: Range: ; Use key ... more

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Vertical asymptote: Domain: Range: ; Use key ... more

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Vertical asymptote: Domain: Range: ; Use key ... more

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Vertical asymptote: Domain: Range: ; The given ... more

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Vertical asymptote: Domain: Range: ; The given ... more

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Vertical asymptote: Domain: Range: ; The given ... more

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Vertical asymptote: Domain: Range: ; The given ... more

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Vertical asymptote: Domain: Range: ; The given ... more

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Vertical asymptote: Domain: Range: ; The given ... more

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Vertical asymptote: Domain: Range: ; The given ... more

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Vertical asymptote: Domain: Range: ; The given ... more

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Vertical asymptote: Domain: Range: ; The given ... more

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Vertical asymptote: Domain: Range: ; The given ... more

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Vertical asymptote: Domain: Range: ; The given ... more

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Vertical asymptote: Domain: Range: ; The given ... more

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Vertical asymptote: Domain: Range: ; The given ... more

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Vertical asymptote: Domain: Range: ; The given ... more

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Vertical asymptote: Domain: Range: ; The given ... more

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Vertical asymptote: Domain: Range: ; The given ... more

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; The logarithm of 0 or a negative number does ... more

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; The logarithm of 0 or a negative number does ... more

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; Find when . ; more

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; The logarithm of 0 or a negative number does ... more

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; The logarithm of 0 or a negative number does ... more

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; The logarithm of 0 or a negative number does ... more

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2 ; The logarithm is a common log (base 10), so ... more

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3 ; The logarithm is a common log (base 10), so ... more

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7 ; The logarithm is a common log (base 10), and ... more

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8 ; The logarithm is a common log (base 10), and ... more

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33 ; The logarithm in the exponent is a common log... more

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53 ; The logarithm in the exponent is a common log... more

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0 ; The general property that applies to all ... more

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1 ; The natural logarithm is log base . Rewrite ... more

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6 ; Use the inverse property that . In other words... more

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7 ; Use the inverse property that . In other words... more

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; To use a property of logarithms, rewrite the ... more

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; To use a property of logarithms, rewrite the ... more

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125 ; Use the inverse property that . In other ... more

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300 ; Use the inverse property that . In other ... more

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; Use the inverse property that . In other words... more

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; Use the inverse property that . In other words... more

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; Use the inverse property that . In other words... more

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; Use the inverse property that . In other words... more

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; The logarithm in the exponent is a common log (... more

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; The logarithm in the exponent is a common log (... more

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10 ; To convert to exponential form, use the ... more

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21 ; To convert to exponential form, use the ... more

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; To convert to exponential form, use the ... more

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16 ; To convert to exponential form, use the ... more

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0 ; Use the property that to simplify the ... more

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1 ; Since the logarithm inside the parentheses is ... more

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2 ; Since the logarithm inside the parentheses is ... more

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0 ; Use the property that to simplify the ... more

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; A logarithm is only defined for positive ... more

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; A logarithm is only defined for positive ... more

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; A logarithm is only defined for positive ... more

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; A logarithm is only defined for positive ... more

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; Since represents age, substitute 13 for each ... more

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; Since represents age, substitute 10 for each ... more

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Approximately 188 decibels;Yes, because 188 is ... more

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65 decibels ; Since represents intensity, ... more

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means . is the base of the logarithm, and it is ... more

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81 is equivalent to 3 raised to what power? ; ... more

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The logarithm of 1 is always 0, regardless of the ... more

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Taking the logarithm base and raising to a power... more

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Reflect the graph of the exponential function over... more

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Set the quantity inside the logarithm (called the ... more

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A population of bunny rabbits will grow quickly at... more

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Evaluate the given function at to find the ... more

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The graph of is a horizontal translation of the ... more

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The graph of is a vertical translation of the ... more

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The graph of is a vertical reflection of the ... more

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The graph of is a translation of the graph of to... more

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The average score drops below 65 after 9 months... more

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(D), (B), (A), (F), (C), (E) ; Construct a ... more

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Makes sense ; The horizontal asymptote of an ... more

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Makes sense ; The expression is equivalent to the... more

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Makes sense ; Since common logarithms are of base ... more

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Does not makes sense ; Substitute and into the ... more

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False; ; Since and , then and , respectively. ... more

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False; is undefined. ; There is no exponent of ... more

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False; The domain of must be . ; The values of ... more

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True ; If , then . That means is equal to the ... more

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; 4 is the exponent of 3 that yields 81. Thus, ... more

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0 ; The expression must be evaluated from the ... more

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; 60 is between and . Thus, takes a value ... more

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Model for boys' height: ; Model for girls' height... more

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Person T: millionPerson L: millionPerson M: ... more

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; Substitute the given values into the difference... more

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; Rewrite as . ; Interchange the role of ... more

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; Apply the change of base property . Take as ... more

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; Apply the change of base property . Take as ... more

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, sum. ; The Product rule distributes the ... more

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; The quotient rule distributes the logarithms of... more

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, multiplication. ; The Power rule is used to take... more

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; Change of base property generally is used for ... more

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; Apply the Product rule to the expression. ; more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of and . ; ; ; ... more

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; Using , determine the value of and . ; ; ; ... more

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; Using , determine the value of , , and . ; ... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Rewrite in exponential form. ; Using , ... more

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; Rewrite in exponential form. ; Using , ... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Rewrite in exponential form. ; Using , ... more

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; Rewrite in exponential form. ; Using , ... more

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; Rewrite in exponential form. ; Using , ... more

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; Rewrite in exponential form. ; Using , ... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Rewrite in exponential form. ; Using , ... more

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; Rewrite in exponential form. ; Using , ... more

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; Using , determine the value of and . ; ; ; Let... more

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; Using , determine the value of and . ; ; ; Let... more

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; Using , determine the value of , , and... more

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; Using , determine the value of , , and... more

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; Since both the bases are equal, use the product... more

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; Since both the bases are equal, use the product... more

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; Use the product rule. ; Simplify. ; more

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; Use the product rule. ; Simplify. ; more

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; Since the bases are equal (both are ), use the ... more

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; Since the bases are equal (both are ), use the ... more

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; Since the bases are equal (both are ), use the ... more

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; Since the bases are equal (both are ), use the ... more

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; Use the power rule. ; Since the bases are equal... more

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; Use the power rule. ; Since the bases are equal... more

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; Use the power rule. ; Use the product rule. ; ... more

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; Apply the power rule for logarithms to the ... more

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; Apply the power rule for logarithms to both ... more

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; Apply the power rule for logarithms to both ... more

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; Apply the power rule for logarithms to both ... more

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; Apply the power rule for logarithms to both ... more

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; Apply the power rule for logarithms to both ... more

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; Apply the power rule for logarithms to both ... more

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; Apply the power rule for logarithms to both ... more

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; Apply the power rule for logarithms to both ... more

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; Apply the power rule for logarithms to , , and... more

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; Apply the power rule for logarithms to , , and... more

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; Apply the distributive law to the product ; ... more

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; Apply the distributive law to the product . ; ... more

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; Apply the distributive law to the product . ; ... more

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; Apply the distributive law to the product . ; ... more

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; Apply the distributive law to multiply among ... more

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; Apply the distributive law to multiply among ... more

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; Factor out into the third and fourth terms of ... more

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; Factor out into the third and fourth terms of ... more

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1.5937 ; Use the change-of-base property for ... more

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1.5812 ; Use the change-of-base property for ... more

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1.6944 ; Use the change-of-base property for ... more

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1.4595 ; Use the change-of-base property for ... more

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–1.2304 ; Use the change-of-base property for ... more

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–2.4456 ; Use the change-of-base property for ... more

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3.6193 ; Use the change-of-base property for ... more

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5.2340 ; Use the change-of-base property for ... more

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Use the change-of-base formula to express the ... more

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Use the change-of-base formula to express the ... more

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Use the change-of-base formula to express the ... more

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Use the change-of-base formula to express the ... more

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; Apply the quotient rule for logarithms to the ... more

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; Express 6 as the product of 2 and 3.Apply the ... more

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; Express 8 as the third power of 2.Apply the ... more

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; Express 81 as the fourth power of 3.Apply the ... more

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; Express 27 as the third power of 3.Rewrite the ... more

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; Express 16 as the fourth power of 2.Rewrite the... more

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False; the expression is equal to 1. ; 1 is the ... more

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False; the expression is undefined. ; In the ... more

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False; ; Apply the product rule for logarithms.... more

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False; ; Use the fact that and apply the product ... more

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True ; Apply the power rule for logarithms. ; more

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False; the expression is equal to . ; 0 is the ... more

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True ; 0 is the exponent of the base that yields ... more

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False; the expression is equal to . ; Apply the ... more

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False; the expression is equal to . ; Apply the ... more

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False; the expression is equal to . ; Apply the ... more

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True  ; Apply the quotient rule for logarithms... more

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True ; Apply the product rule for logarithms. ; more

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True  ; Use the change-of-base property for ... more

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False. is not the reciprocal of .  Change to to... more

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The value of a logarithm that contains a product ... more

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The value of a logarithm that contains a quotient ... more

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The value of a logarithm that contains a power can... more

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Apply the power rule for logarithms to the second ... more

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The property makes it possible to change a ... more

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Divide by .  Key in these values into a ... more

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The student is talking about the logarithm of a ... more

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 The series gets closer to the value of . ; Key in... more

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The function is moved 1 unit up the -axis to ... more

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This reasoning makes sense because the properties ... more

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This reasoning makes sense because the rules for ... more

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This reasoning makes sense because and are ... more

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This reasoning does not make sense. The steps ... more

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127.3 million ; Compute the number of years from ... more

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2012 ; Substitute 7 for , and solve the equation ... more

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 -intercept: Vertical asymptote: Domain: Range: ; ... more

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In 2014 there will be about 385 million purchased... more

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Linear for high forecastLogarithmic for medium ... more

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; Write the logarithmic equation in exponential ... more

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; To solve for , isolate on one side of the ... more

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; Express the left side as a single term. Apply ... more

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; Express the left side as a single term. Apply ... more

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120 decibels ; Substitute for . ; Solve for .... more

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; Apply the power rule, that is, write as , ... more

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1 ; since is obtained when the base is raised to... more

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0 ; since 1 is obtained when the base 6 is raised ... more

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investment at ; ; Solve for the final amount, ... more

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13.9 years ; Use to find , where , , , and . ... more

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; Use to find , where , , and . Start by ... more

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; Let be the population of continent A. Use the ... more

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12.5 days ; Let be the initial amount of the ... more

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linear ; From the table of values, observe that ... more

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logarithmic ; From the table of values, observe ... more

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exponential ; From the table of values, observe ... more

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quadratic ; From the table of values, observe that... more

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; Isolate the power on one side. Divide both ... more

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; Remove the absolute-value bars by writing as ... more

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; Isolate one radical by adding to both sides.... more

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; Find all possible roots of the equation, where... more

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; Isolate the exponential expression on one side ... more

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; Express the left side as a single expression by... more

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; Express the left side as a single expression by... more

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; Isolate the -term on one side by subtracting 14... more

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; Remove the absolute-value bars by writing as... more

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Find the -intercept. Let , and solve for . Since ... more

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The equation follows the form , which is a ... more

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Find the -intercept. Let , and solve for . ; Set ... more

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Identify the degree of the polynomial function and... more

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Find the . Change with , and replace with and ... more

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Find the value of and corresponding to each ... more

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; ; Find the slope of the line using the two given... more

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; ; Evaluate . ; Evaluate . ; more

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2 hours ; Let be the number of sleeping hours and... more

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2 seconds; 69 feet ; The given equation is a ... more

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4.1 seconds ; Substitute 0 for . ; Solve for ... more

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; Given a 50-hour work last week, you worked a ... more

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