Question 1

Write the equation in its equivalent exponential form.
-$\log _ { 3 } 9 = 2$

Accepted Answer

A)  $92 = 3$ 
B)  $3 ^ { 9 } = 2$ 
C)  $2 ^ { 3 } = 9$ 
D)  $3 ^ { 2 } = 9$ 
A)  $92 = 3$ 
B)  $3 ^ { 9 } = 2$ 
C)  $2 ^ { 3 } = 9$ 
D)  $3 ^ { 2 } = 9$

Question 2

Evaluate or simplify the expression without using a calculator.
-ln$\sqrt [ 6 ] { e }$

Accepted Answer

A)  $\frac { 1 } { 6 }$ 
B)  6 
C)  $6 \mathrm { e }$ 
D)  $\frac { \mathrm { e } } { 6 }$ 
A)  $\frac { 1 } { 6 }$ 
B)  6 
C)  $6 \mathrm { e }$ 
D)  $\frac { \mathrm { e } } { 6 }$

Question 3

Find the domain of the logarithmic function.
-$$f ( x ) = \ln \left( \frac { 1 } { x + 10 } \right)$$

Accepted Answer

A)  $( - 10 , \infty )$ 
B)  $( 1 , \infty )$ 
C)  $( 0 , \infty )$ 
D)  $( 10 , \infty )$ 
A)  $( - 10 , \infty )$ 
B)  $( 1 , \infty )$ 
C)  $( 0 , \infty )$ 
D)  $( 10 , \infty )$

Question 4

The graph of an exponential function is given. Select the function for the graph from the functions listed.
-

Accepted Answer

A)  $f ( x ) = - 4 ^ { - x }$ 
B)  $f ( x ) = 4 ^ { - x }$ 
C)  $f ( x ) = 4 ^ { x }$ 
D)  $f ( x ) = - 4 ^ { x }$ 
A)  $f ( x ) = - 4 ^ { - x }$ 
B)  $f ( x ) = 4 ^ { - x }$ 
C)  $f ( x ) = 4 ^ { x }$ 
D)  $f ( x ) = - 4 ^ { x }$

Question 5

$$\text { Use the compound interest formulas } A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
-Suppose that you have $3000 to invest. Which investment yields the greater return over 9 years: 5.4% compounded monthly or 5.5% compounded quarterly?

Accepted Answer

A) $3000 invested at 5.4% compounded monthly over 9 years yields the greater return. 
B) Both investment plans yield the same return. 
C) $3000 invested at 5.5% compounded quarterly over 9 years yields the greater return. 
A) $3000 invested at 5.4% compounded monthly over 9 years yields the greater return. 
B) Both investment plans yield the same return. 
C) $3000 invested at 5.5% compounded quarterly over 9 years yields the greater return.

Question 6

Evaluate or simplify the expression without using a calculator.
-$\log \left( \frac { 1 } { 1000 } \right)$

Accepted Answer

A)  $\frac { 1 } { 1000 }$ 
B)  3 
C)  $- 3$ 
D)  $- \frac { 1 } { 3 }$ 
A)  $\frac { 1 } { 1000 }$ 
B)  3 
C)  $- 3$ 
D)  $- \frac { 1 } { 3 }$

Question 7

Find the domain of the logarithmic function.
-$$f ( x ) = \log _ { 8 } ( x + 6 )$$

Accepted Answer

A)  $( - \infty , 0 )$ or $( 0 , \infty )$ 
B)  $( 8 , \infty )$ 
C)  $( 6 , \infty )$ 
D)  $( - 6 , \infty )$ 
A)  $( - \infty , 0 )$ or $( 0 , \infty )$ 
B)  $( 8 , \infty )$ 
C)  $( 6 , \infty )$ 
D)  $( - 6 , \infty )$

Question 8

Evaluate the expression without using a calculator.
-$e ^ { \ln 271 }$

Accepted Answer

A)  $\ln 271$ 
B)  271 
C)  $\mathrm { e } ^ { 271 }$ 
D)  $- 271$ 
A)  $\ln 271$ 
B)  271 
C)  $\mathrm { e } ^ { 271 }$ 
D)  $- 271$

Question 9

Find the domain of the logarithmic function.
-$f ( x ) = \ln ( 2 - x )$

Accepted Answer

A)  $( - \infty , 2 )$ 
B)  $( - \infty , 2 )$ or $( 2 , \infty )$ 
C)  $( - 2 , \infty )$ 
D)  $( - \infty , 0 )$ 
A)  $( - \infty , 2 )$ 
B)  $( - \infty , 2 )$ or $( 2 , \infty )$ 
C)  $( - 2 , \infty )$ 
D)  $( - \infty , 0 )$

Question 10

Evaluate the expression without using a calculator.
-$\mathrm { e } ^ { \ln 9 x ^ { 3 } }$

Accepted Answer

A)  $\ln 9 x ^ { 3 }$ 
B)  $\mathrm { e } ^ { 9 \mathrm { x } ^ { 3 } }$ 
C)  $9 x ^ { 3 }$ 
D)  3 
A)  $\ln 9 x ^ { 3 }$ 
B)  $\mathrm { e } ^ { 9 \mathrm { x } ^ { 3 } }$ 
C)  $9 x ^ { 3 }$ 
D)  3

Question 11

Evaluate the expression without using a calculator.
-$\log _ { 6 } \frac { 1 } { \sqrt { 6 } }$

Accepted Answer

A)  $- \frac { 1 } { 2 }$ 
B)  $- \frac { 1 } { 6 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 1 } { 6 }$ 
A)  $- \frac { 1 } { 2 }$ 
B)  $- \frac { 1 } { 6 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 1 } { 6 }$

Question 12

Approximate the number using a calculator. Round your answer to three decimal places.
-$2.4 ^ { \pi }$

Accepted Answer

A)  $15.648$ 
B)  $15.601$ 
C)  $36.462$ 
D)  $7.540$ 
A)  $15.648$ 
B)  $15.601$ 
C)  $36.462$ 
D)  $7.540$

Question 13

Evaluate or simplify the expression without using a calculator.
-$10 \log \sqrt [ 5 ] { x }$

Accepted Answer

A)  5 
B)  $x ^ { - 1 / 5 }$ 
C)  $x ^ { 1 / 5 }$ 
D)  $x ^ { 5 }$ 
A)  5 
B)  $x ^ { - 1 / 5 }$ 
C)  $x ^ { 1 / 5 }$ 
D)  $x ^ { 5 }$

Question 14

Solve the problem.
-The size of the raccoon population at a national park increases at the rate of $4.3 \%$ per year. If the size of the current population is 157 , find how many raccoons there should be in 4 years. Use the function $f ( x ) = 157 e 0.043 t$ and round to the nearest whole number.

Accepted Answer

A)  184 
B)  190 
C)  188 
D)  186 
A)  184 
B)  190 
C)  188 
D)  186

Question 15

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 2 } \left( \frac { 8 } { x } \right)$

Accepted Answer

A)  $6 - \log _ { 2 } x$ 
B)  $- 3 \log _ { 2 } x$ 
C)  $3 - \log _ { 2 } x$ 
D)  $\frac { 3 } { x }$ 
A)  $6 - \log _ { 2 } x$ 
B)  $- 3 \log _ { 2 } x$ 
C)  $3 - \log _ { 2 } x$ 
D)  $\frac { 3 } { x }$

Question 16

The graph of an exponential function is given. Select the function for the graph from the functions listed.
-

Accepted Answer

A)  $f ( x ) = 2 ^ { - x }$ 
B)  $f ( x ) = 2 ^ { x }$ 
C)  $f ( x ) = - 2 ^ { - x }$ 
D)  $f ( x ) = - 2 ^ { x }$ 
A)  $f ( x ) = 2 ^ { - x }$ 
B)  $f ( x ) = 2 ^ { x }$ 
C)  $f ( x ) = - 2 ^ { - x }$ 
D)  $f ( x ) = - 2 ^ { x }$

Question 17

Write the equation in its equivalent exponential form.
-$\log _ { 2 } 32 = x$

Accepted Answer

A)  $32 ^ { x } = 2$ 
B)  $32 ^ { 2 } = x$ 
C)  $x ^ { 2 } = 32$ 
D)  $2 ^ { x } = 32$ 
A)  $32 ^ { x } = 2$ 
B)  $32 ^ { 2 } = x$ 
C)  $x ^ { 2 } = 32$ 
D)  $2 ^ { x } = 32$

Question 18

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$$\log _ { 3 } \left( \frac { 7 } { 13 } \right)$$

Accepted Answer

A)  $\log _ { 3 } 7 - \log _ { 3 } 13$ 
B)  $\log _ { 3 } 13 - \log _ { 3 } 7$ 
C)  $\log _ { 3 } 7 + \log _ { 3 } 13$ 
D)  $\frac { \log _ { 3 } 7 } { \log _ { 3 } 13 }$ 
A)  $\log _ { 3 } 7 - \log _ { 3 } 13$ 
B)  $\log _ { 3 } 13 - \log _ { 3 } 7$ 
C)  $\log _ { 3 } 7 + \log _ { 3 } 13$ 
D)  $\frac { \log _ { 3 } 7 } { \log _ { 3 } 13 }$

Question 19

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$$\log _ { 5 } 7 ^ { - 3 }$$

Accepted Answer

A)  $7 \log _ { 5 } 3$ 
B)  $- 3 \log _ { 5 } 7$ 
C)  $5 \log _ { 3 } 7$ 
D)  $- 15 \log 7$ 
A)  $7 \log _ { 5 } 3$ 
B)  $- 3 \log _ { 5 } 7$ 
C)  $5 \log _ { 3 } 7$ 
D)  $- 15 \log 7$

Question 20

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 5 } ( 25 x )$

Accepted Answer

A)  $2 + \log _ { 5 } x$ 
B)  $2 \mathrm { x }$ 
C)  $10 + \log _ { 5 } x$ 
D)  $2 \log _ { 5 } x$ 
A)  $2 + \log _ { 5 } x$ 
B)  $2 \mathrm { x }$ 
C)  $10 + \log _ { 5 } x$ 
D)  $2 \log _ { 5 } x$

Write the equation in its equivalent exponential form. - $\log _ { 3 } 9 = 2$

Evaluate or simplify the expression without using a calculator. -ln $\sqrt [ 6 ] { e }$

Find the domain of the logarithmic function. - $f ( x ) = \ln \left( \frac { 1 } { x + 10 } \right)$

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Evaluate or simplify the expression without using a calculator. - $\log \left( \frac { 1 } { 1000 } \right)$

Find the domain of the logarithmic function. - $f ( x ) = \log _ { 8 } ( x + 6 )$

Evaluate the expression without using a calculator. - $e ^ { \ln 271 }$

Find the domain of the logarithmic function. - $f ( x ) = \ln ( 2 - x )$

Evaluate the expression without using a calculator. - $\mathrm { e } ^ { \ln 9 x ^ { 3 } }$

Evaluate the expression without using a calculator. - $\log _ { 6 } \frac { 1 } { \sqrt { 6 } }$

Approximate the number using a calculator. Round your answer to three decimal places. - $2.4 ^ { \pi }$

Evaluate or simplify the expression without using a calculator. - $10 \log \sqrt [ 5 ] { x }$

Solve the problem. -The size of the raccoon population at a national park increases at the rate of $4.3 \%$ per year. If the size of the current population is 157 , find how many raccoons there should be in 4 years. Use the function $f ( x ) = 157 e 0.043 t$ and round to the nearest whole number.

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 2 } \left( \frac { 8 } { x } \right)$

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Write the equation in its equivalent exponential form. - $\log _ { 2 } 32 = x$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } \left( \frac { 7 } { 13 } \right)$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 5 } 7 ^ { - 3 }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 5 } ( 25 x )$

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Systems of Equations and Inequalities

Filters

Exam 4: Exponential and Logarithmic Functions

Write the equation in its equivalent exponential form. - log⁡39=2\log _ { 3 } 9 = 2log3​9=2

Evaluate or simplify the expression without using a calculator. -ln e6\sqrt [ 6 ] { e }6e​

Find the domain of the logarithmic function. - f(x)=ln⁡(1x+10)f ( x ) = \ln \left( \frac { 1 } { x + 10 } \right)f(x)=ln(x+101​)

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Evaluate or simplify the expression without using a calculator. - log⁡(11000)\log \left( \frac { 1 } { 1000 } \right)log(10001​)

Find the domain of the logarithmic function. - f(x)=log⁡8(x+6)f ( x ) = \log _ { 8 } ( x + 6 )f(x)=log8​(x+6)

Evaluate the expression without using a calculator. - eln⁡271e ^ { \ln 271 }eln271

Find the domain of the logarithmic function. - f(x)=ln⁡(2−x)f ( x ) = \ln ( 2 - x )f(x)=ln(2−x)

Evaluate the expression without using a calculator. - eln⁡9x3\mathrm { e } ^ { \ln 9 x ^ { 3 } }eln9x3

Evaluate the expression without using a calculator. - log⁡616\log _ { 6 } \frac { 1 } { \sqrt { 6 } }log6​6​1​

Approximate the number using a calculator. Round your answer to three decimal places. - 2.4π2.4 ^ { \pi }2.4π

Evaluate or simplify the expression without using a calculator. - 10log⁡x510 \log \sqrt [ 5 ] { x }10log5x​

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡2(8x)\log _ { 2 } \left( \frac { 8 } { x } \right)log2​(x8​)

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Write the equation in its equivalent exponential form. - log⁡232=x\log _ { 2 } 32 = xlog2​32=x

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡3(713)\log _ { 3 } \left( \frac { 7 } { 13 } \right)log3​(137​)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡57−3\log _ { 5 } 7 ^ { - 3 }log5​7−3

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡5(25x)\log _ { 5 } ( 25 x )log5​(25x)

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Systems of Equations and Inequalities

Filters

Write the equation in its equivalent exponential form. - $\log _ { 3 } 9 = 2$

Evaluate or simplify the expression without using a calculator. -ln $\sqrt [ 6 ] { e }$

Find the domain of the logarithmic function. - $f ( x ) = \ln \left( \frac { 1 } { x + 10 } \right)$

Evaluate or simplify the expression without using a calculator. - $\log \left( \frac { 1 } { 1000 } \right)$

Find the domain of the logarithmic function. - $f ( x ) = \log _ { 8 } ( x + 6 )$

Evaluate the expression without using a calculator. - $e ^ { \ln 271 }$

Find the domain of the logarithmic function. - $f ( x ) = \ln ( 2 - x )$

Evaluate the expression without using a calculator. - $\mathrm { e } ^ { \ln 9 x ^ { 3 } }$

Evaluate the expression without using a calculator. - $\log _ { 6 } \frac { 1 } { \sqrt { 6 } }$

Approximate the number using a calculator. Round your answer to three decimal places. - $2.4 ^ { \pi }$

Evaluate or simplify the expression without using a calculator. - $10 \log \sqrt [ 5 ] { x }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 2 } \left( \frac { 8 } { x } \right)$

Write the equation in its equivalent exponential form. - $\log _ { 2 } 32 = x$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } \left( \frac { 7 } { 13 } \right)$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 5 } 7 ^ { - 3 }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 5 } ( 25 x )$