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Exam 14: Exponential and Logarithmic Functions

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Question 51

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Given that log 8 5 = 0.7740 and log 8 11 = 1.1531, evaluate the expression $\log _ { 8 } \sqrt [ 6 ] { 5 }$ by using properties: For positive real numbers b , r and s , where b $\neq$ 1, and for any real number p , $\log b r s = \log b r + \log b s$ $\log b \frac { r } { s } = \log b r - \log b s$ $\log b r ^ { p } = p ( \log b r )$

A) 0.1011
B) 0.0749
C) 0.1253
D) 0.1290

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Question 52

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Express the following as a single logarithm. (Assume that all variables represent positive real numbers.) $4 \log b x + \frac { 1 } { 2 } \log b ( x - 1 ) - 6 \log _ { b } ( 4 x + 8 )$

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Question 53

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Solve the equation. $10 ^ { x } = 0.1$

Use the formula $A = p e ^ { r t }$ to find the total amount of money accumulated at the end of the indicated time period by compounding continuously: $6,750 for 11 years at 9.5%. The choices are rounded to the nearest cent.

Express the following as a single logarithm. (Assume that all variables represent positive real numbers.) 2 log b x + 9 log b y $-$ 6 log b z

Solve the equation. $\log 625 x = \frac { 5 } { 4 }$

Use a calculator to find each common logarithm. Express answer to four decimal places. $\ln 8$

Write 10 ^{- 4} = 0.0001 in logarithmic form.

Solve the equation. $\text { (4) } \left( 2 ^ { x } \right) = 8 ^ { x }$

Given that log 8 5 = 0.7740 and log 8 11 = 1.1531, evaluate the expression $\log 8 \left( \frac { 5 } { 11 } \right)$ by using properties: For positive real numbers b , r and s , where b $\neq$ 1, and for any real number p , $\log b^{ r s} = \log b^ r + \log b ^s$ $\log b \frac { r } { s } = \log b r - \log b s$ $\log b r ^ { p } = p ( \log b r )$ Please give the answer to four decimal places.

Write 10 ^{- 3} = 0.001 in logarithmic form.

Determine whether the function f is one-to-one. f ( x ) = | x | + 7 Please enter yes or no .

Solve the exponential equation and express approximate solutions to the nearest hundredth. 9 ^x + 6 = 40

Solve the equation. $3 ^ { 3 x - 2 } = 3$

Solve the equation. $\left( 3 ^ { x + 5 } \right) \left( 3 ^ { x } \right) = 81$

Find f -1 ( x ). f ( x ) = x $-$ 3

Write the logarithmic statement in exponential form. log 10 0.00001 = $-$ 5

Use a graphing calculator to graph the exponential functions $f ( x ) = ( 2.5 ) ^ { x } \text { and } f ( x ) = ( 0.3 ) ^ { x }$ on the same set of axes. Choose the answer from the following (the blue curve represents f ( x ) = (2.5) x and the red curve represents f ( x ) = (0.3) x ) .

Form the inverse function f ^{- -1}, and list the domain and range of f ^{- -1}. f = {(1, 6) , (4, 8) , (6, 50) } Match the name of each set with the corresponding set. - $\{ ( 6,1 ) , ( 8,4 ) , ( 50,6 ) \}$

Use your calculator to find x when given ln x . $\ln x = 0.8926$ Please round the answer to the nearest hundredth.