Question 1

Evaluate.
-$$7 ( \sqrt [ 5 ] { 16 } ) ^ { \log _ { 2 } 7 }$$

Accepted Answer

A) 14 
B) 112 
C) 49 
D) 7 
A) 14 
B) 112 
C) 49 
D) 7

Question 2

Solve the problem.
-Luis invests $1000 into an account earning interest at a rate of 7% compounded annually. Find the amount in the account at the end of 10 years.

Accepted Answer

A) $1967.15 
B) $1838.46 
C) $2104.85 
D) $967.15 
A) $1967.15 
B) $1838.46 
C) $2104.85 
D) $967.15

Question 3

Write as a logarithm of a single expression.
-$3 \log _ { 5 } 3 + \frac { 1 } { 7 } \log _ { 5 } ( r - 7 ) - \frac { 1 } { 2 } \log _ { 5 } r$

Accepted Answer

A)  $\log _5 \frac { 27 \sqrt [ 7 ] { r - 7 } } { \sqrt { r } }$ 
B)  $\log _5 \left( \frac { 3 } { 14 } \sqrt { \frac { r - 7 } { r } } \right)$ 
C)  $\log _ { 5 } \sqrt { \frac { 3 r - 21 } { 14 r } }$ 
D)  $\log _5 \frac { 27 r - 7 } { 14 r }$ 
A)  $\log _5 \frac { 27 \sqrt [ 7 ] { r - 7 } } { \sqrt { r } }$ 
B)  $\log _5 \left( \frac { 3 } { 14 } \sqrt { \frac { r - 7 } { r } } \right)$ 
C)  $\log _ { 5 } \sqrt { \frac { 3 r - 21 } { 14 r } }$ 
D)  $\log _5 \frac { 27 r - 7 } { 14 r }$

Question 4

The following equation is in the forming equation is in the form $\mathrm { P } = \mathrm { P } _ { 0 } \mathrm { e } ^ { \mathrm { kt } }$ . Solve the equation for the remaining variable. Remember, e is a
constant.
-$\mathrm { P } = 190 \mathrm { e } ^ { 2.4 ( 1.1 ) }$

Accepted Answer

A)  $P \approx 2662.51$ 
B)  $\mathrm { P } \approx 80.1$ 
C)  $P \approx 501.6$ 
D)  $\mathrm { P } \approx 2303.84$ 
A)  $P \approx 2662.51$ 
B)  $\mathrm { P } \approx 80.1$ 
C)  $P \approx 501.6$ 
D)  $\mathrm { P } \approx 2303.84$

Question 5

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places.
-150

Accepted Answer

A) 5.0106 
B) 2.1732 
C) 2.1761 
D) 2.1790 
A) 5.0106 
B) 2.1732 
C) 2.1761 
D) 2.1790

Question 6

Determine whether the given functions are inverses of each other.
-$$f ( x ) = 7 x , \quad g ( x ) = \frac { x } { 7 }$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 7

Write the equation in exponential form.
-$\log _ { 1 / 2 } 4 = - 2$

Accepted Answer

A)  $( - 2 ) ^ { 1 / 2 } = 4$ 
B)  $\left( \frac { 1 } { 2 } \right) ^ { - 2 } = 4$ 
C)  $\left( \frac { 1 } { 2 } \right) ^ { 2 } = 4$ 
D)  $4 ^ { 1 / 2 } = 2$ 
A)  $( - 2 ) ^ { 1 / 2 } = 4$ 
B)  $\left( \frac { 1 } { 2 } \right) ^ { - 2 } = 4$ 
C)  $\left( \frac { 1 } { 2 } \right) ^ { 2 } = 4$ 
D)  $4 ^ { 1 / 2 } = 2$

Question 8

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth.
-$$\log _ { 9 } ( 5 x - 3 ) = \log _ { 9 } ( 3 x + 7 )$$

Accepted Answer

A) 2 
B) 5 
C) 4 
D) no solution 
A) 2 
B) 5 
C) 4 
D) no solution

Question 9

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.
-$f ( x ) = \sqrt { x - 1 } , x \geq 1$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 1 , \mathrm { x } \geq 0$ 
B)  $f ^ { - 1 } ( x ) = ( x - 1 ) ^ { 2 } , x \geq 1$ 
C)  $f^{-1}(x)=x^{2}+1, x \geq 0$ 
D) not a one-to-one function 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 1 , \mathrm { x } \geq 0$ 
B)  $f ^ { - 1 } ( x ) = ( x - 1 ) ^ { 2 } , x \geq 1$ 
C)  $f^{-1}(x)=x^{2}+1, x \geq 0$ 
D) not a one-to-one function

Question 10

Write the equation in exponential form.
-$\log _ { 2 } 8 = 3$

Accepted Answer

A)  $3 ^ { 2 } = 8$ 
B)  $2 ^ { 3 } = 8$ 
C)  $8 ^ { 3 } = 2$ 
D)  $2 ^ { 8 } = 3$ 
A)  $3 ^ { 2 } = 8$ 
B)  $2 ^ { 3 } = 8$ 
C)  $8 ^ { 3 } = 2$ 
D)  $2 ^ { 8 } = 3$

Question 11

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth.
-$$\log _ { 2 } x = - 3$$

Accepted Answer

A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 1 } { 6 }$ 
C) -8 
D) 8 
A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 1 } { 6 }$ 
C) -8 
D) 8

Question 12

Use a calculator to solve the equation. Round the answer to the nearest hundredth.
-$$3 ^ { x + 6 } = 3$$

Accepted Answer

A) -0.78 
B) -5.00 
C) 1.78 
D) 7.00 
A) -0.78 
B) -5.00 
C) 1.78 
D) 7.00

Question 13

Use a calculator to solve the equation. Round the answer to the nearest hundredth.
-$$5 ^ { x } = 2 ^ { x + 1 }$$

Accepted Answer

A) 0.36 
B) 0.76 
C) 0.30 
D) 0.63 
A) 0.36 
B) 0.76 
C) 0.30 
D) 0.63

Question 14

Write the equation in logarithmic form.
-$e ^ { - 1 / 2 } = 0.6065$

Accepted Answer

A)  $- \frac { 1 } { 2 }$ 
B)  $\log _e \left( - \frac { 1 } { 2 } \right) = 0.6065$ 
C)  $\log _ { 0.6065 } \left( - \frac { 1 } { 2 } \right) = \mathrm { e }$ 
D)  $\log _ { 0.6065 }e = - \frac { 1 } { 2 }$ 
A)  $- \frac { 1 } { 2 }$ 
B)  $\log _e \left( - \frac { 1 } { 2 } \right) = 0.6065$ 
C)  $\log _ { 0.6065 } \left( - \frac { 1 } { 2 } \right) = \mathrm { e }$ 
D)  $\log _ { 0.6065 }e = - \frac { 1 } { 2 }$

Question 15

For the given functions f and g , find the indicated composition.
-$$\begin{array} { l } 
f ( x ) = 4 x ^ { 2 } + 3 x + 4 , \quad g ( x ) = 3 x - 6 \
( g \circ f ) ( x )
\end{array}$$

Accepted Answer

A)  $4 x ^ { 2 } + 9 x + 6$ 
B)  $12 x ^ { 2 } + 9 x + 6$ 
C)  $4 x ^ { 2 } + 3 x - 2$ 
D)  $12 x ^ { 2 } + 9 x + 18$ 
A)  $4 x ^ { 2 } + 9 x + 6$ 
B)  $12 x ^ { 2 } + 9 x + 6$ 
C)  $4 x ^ { 2 } + 3 x - 2$ 
D)  $12 x ^ { 2 } + 9 x + 18$

Question 16

Evaluate.
-$\log _ { 17 } 17$

Accepted Answer

A)  $\frac { 1 } { 17 }$ 
B) 0 
C) 1 
D) 17 
A)  $\frac { 1 } { 17 }$ 
B) 0 
C) 1 
D) 17

Question 17

Find the following value. Round to four decimal places.
-ln 0.29412

Accepted Answer

A) -0.5315 
B) -1.2238 
C) 1 
D) 1.3419 
A) -0.5315 
B) -1.2238 
C) 1 
D) 1.3419

Question 18

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$\log_ 5 \frac { d ^ { 4 } } { ( c - 5 ) ^ { 2 } }$

Accepted Answer

A)  $4 \log _ { 5 } d - 2 \log _ { 5 } ( c - 5 )$ 
B)  $\frac { 4 \log _ { 5 } d } { 2 \log _ { 5 } ( c - 5 ) }$ 
C)  $\frac { 4 \log _ { 5 } \mathrm {~d} } { 2 \log _ { 5 } c~ - ~2 \log _ { 5 } 5 }$ 
D)  $2 \left( \log _ { 5 } d - \log_ 5 ( c - 5 ) \right)$ 
A)  $4 \log _ { 5 } d - 2 \log _ { 5 } ( c - 5 )$ 
B)  $\frac { 4 \log _ { 5 } d } { 2 \log _ { 5 } ( c - 5 ) }$ 
C)  $\frac { 4 \log _ { 5 } \mathrm {~d} } { 2 \log _ { 5 } c~ - ~2 \log _ { 5 } 5 }$ 
D)  $2 \left( \log _ { 5 } d - \log_ 5 ( c - 5 ) \right)$

Question 19

Write as a logarithm of a single expression.
-$\left( \log _ { a } m - \log _ { a } n \right) + 2 \log _ { a } k$

Accepted Answer

A)  $\log _ { a } \frac { m } { k ^ { 2 } n }$ 
B)  $\log _ { a } m k^ { 2 } n$ 
C)  $\log _ { a } \frac { 2 m k } { n }$ 
D)  $\log _ { a } \frac { m k ^ { 2 } } { n }$ 
A)  $\log _ { a } \frac { m } { k ^ { 2 } n }$ 
B)  $\log _ { a } m k^ { 2 } n$ 
C)  $\log _ { a } \frac { 2 m k } { n }$ 
D)  $\log _ { a } \frac { m k ^ { 2 } } { n }$

Question 20

Graph the function.
-$f ( x ) = 3 ^ { x }$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Evaluate. - $7 ( \sqrt [ 5 ] { 16 } ) ^ { \log _ { 2 } 7 }$

Solve the problem. -Luis invests $1000 into an account earning interest at a rate of 7% compounded annually. Find the amount in the account at the end of 10 years.

Write as a logarithm of a single expression. - $3 \log _ { 5 } 3 + \frac { 1 } { 7 } \log _ { 5 } ( r - 7 ) - \frac { 1 } { 2 } \log _ { 5 } r$

The following equation is in the forming equation is in the form $\mathrm { P } = \mathrm { P } _ { 0 } \mathrm { e } ^ { \mathrm { kt } }$ . Solve the equation for the remaining variable. Remember, e is a constant. - $\mathrm { P } = 190 \mathrm { e } ^ { 2.4 ( 1.1 ) }$

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places. -150

Determine whether the given functions are inverses of each other. - $f ( x ) = 7 x , \quad g ( x ) = \frac { x } { 7 }$

Write the equation in exponential form. - $\log _ { 1 / 2 } 4 = - 2$

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - $\log _ { 9 } ( 5 x - 3 ) = \log _ { 9 } ( 3 x + 7 )$

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. - $f ( x ) = \sqrt { x - 1 } , x \geq 1$

Write the equation in exponential form. - $\log _ { 2 } 8 = 3$

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - $\log _ { 2 } x = - 3$

Use a calculator to solve the equation. Round the answer to the nearest hundredth. - $3 ^ { x + 6 } = 3$

Use a calculator to solve the equation. Round the answer to the nearest hundredth. - $5 ^ { x } = 2 ^ { x + 1 }$

Write the equation in logarithmic form. - $e ^ { - 1 / 2 } = 0.6065$

For the given functions f and g , find the indicated composition. - f(x)=4+3x+4,g(x)=3x-6 (g\circf)(x)

Evaluate. - $\log _ { 17 } 17$

Find the following value. Round to four decimal places. -ln 0.29412

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log_ 5 \frac { d ^ { 4 } } { ( c - 5 ) ^ { 2 } }$

Write as a logarithm of a single expression. - $\left( \log _ { a } m - \log _ { a } n \right) + 2 \log _ { a } k$

Graph the function. - $f ( x ) = 3 ^ { x }$ $Graph the function. - f ( x ) = 3 ^ { x }$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Exam 9: Exponential and Logarithmic Functions

Evaluate. - 7(165)log⁡277 ( \sqrt [ 5 ] { 16 } ) ^ { \log _ { 2 } 7 }7(516​)log2​7

Solve the problem. -Luis invests $1000 into an account earning interest at a rate of 7% compounded annually. Find the amount in the account at the end of 10 years.

Write as a logarithm of a single expression. - 3log⁡53+17log⁡5(r−7)−12log⁡5r3 \log _ { 5 } 3 + \frac { 1 } { 7 } \log _ { 5 } ( r - 7 ) - \frac { 1 } { 2 } \log _ { 5 } r3log5​3+71​log5​(r−7)−21​log5​r

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places. -150

Determine whether the given functions are inverses of each other. - f(x)=7x,g(x)=x7f ( x ) = 7 x , \quad g ( x ) = \frac { x } { 7 }f(x)=7x,g(x)=7x​

Write the equation in exponential form. - log⁡1/24=−2\log _ { 1 / 2 } 4 = - 2log1/2​4=−2

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - log⁡9(5x−3)=log⁡9(3x+7)\log _ { 9 } ( 5 x - 3 ) = \log _ { 9 } ( 3 x + 7 )log9​(5x−3)=log9​(3x+7)

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. - f(x)=x−1,x≥1f ( x ) = \sqrt { x - 1 } , x \geq 1f(x)=x−1​,x≥1

Write the equation in exponential form. - log⁡28=3\log _ { 2 } 8 = 3log2​8=3

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - log⁡2x=−3\log _ { 2 } x = - 3log2​x=−3

Use a calculator to solve the equation. Round the answer to the nearest hundredth. - 3x+6=33 ^ { x + 6 } = 33x+6=3

Use a calculator to solve the equation. Round the answer to the nearest hundredth. - 5x=2x+15 ^ { x } = 2 ^ { x + 1 }5x=2x+1

Write the equation in logarithmic form. - e−1/2=0.6065e ^ { - 1 / 2 } = 0.6065e−1/2=0.6065