Question 1

Solve the equation.
-$$\log _ { 3 } ( x - 1 ) + \log _ { 3 } ( x - 7 ) = 3$$

Accepted Answer

A) -2 
B) 10 
C) 10, -2 
D) 11 
A) -2 
B) 10 
C) 10, -2 
D) 11

Question 2

Use the change of base formula to find the value of the following logarithm. Do not round logarithms in the change of
base formula. Write the answer rounded to the nearest ten-thousandth.
-$$\log _ { 4 } 0.069$$

Accepted Answer

A) -4.6446 
B) 0.0415 
C) -0.5185 
D) -1.9286 
A) -4.6446 
B) 0.0415 
C) -0.5185 
D) -1.9286

Question 3

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places.
-3.26

Accepted Answer

A) 0.5132 
B) 1.1817 
C) 0.4997 
D) 0.5263 
A) 0.5132 
B) 1.1817 
C) 0.4997 
D) 0.5263

Question 4

Find the common logarithm of the number. Round answer to four decimal places.
-log 0.00281

Accepted Answer

A) -2.5361 
B) -2.5670 
C) -2.5513 
D) -5.8746 
A) -2.5361 
B) -2.5670 
C) -2.5513 
D) -5.8746

Question 5

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.
-$f ( x ) = x ^ { 2 } - 7$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 7$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 2 } - 7$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 7$ 
D) not a one-to-one function 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 7$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 2 } - 7$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 7$ 
D) not a one-to-one function

Question 6

Find the number N. Round N to six decimal places.
-log N = 2.5224

Accepted Answer

A) 332.966085 
B) 0.080267 
C) 0.003003 
D) 1.787475 
A) 332.966085 
B) 0.080267 
C) 0.003003 
D) 1.787475

Question 7

Write as a logarithm of a single expression.
-$\log _ { 6 } ( x + 2 ) - \log _ { 6 } ( x + 7 )$

Accepted Answer

A)  $\log _ { 6 } 5$ 
B)  $\log _ { 6 } \left( \frac { x + 2 } { x - 7 } \right)$ 
C)  $\log _ { 6 } \left( x ^ { 2 } + 9 x + 14 \right)$ 
D)  $\log _ { 6 } \left( \frac { x + 2 } { x + 7 } \right)$ 
A)  $\log _ { 6 } 5$ 
B)  $\log _ { 6 } \left( \frac { x + 2 } { x - 7 } \right)$ 
C)  $\log _ { 6 } \left( x ^ { 2 } + 9 x + 14 \right)$ 
D)  $\log _ { 6 } \left( \frac { x + 2 } { x + 7 } \right)$

Question 8

Solve the problem.
-The Richter Scale measures the magnitude M of an earthquake. An earthquake whose seismographic reading measures x millimeters 100 kilometers from the epicenter has magnitude M given byven by $M ( x ) = \log \left( \frac { x } { 10 ^ { - 3 } } \right)$ . Give Giv
The magnitude of an earthquake that resulted in a seismographic reading of 99,236 millimeters 100 kilometers
From its epicenter. Round to the nearest tenth.

Accepted Answer

A) 9.0 
B) 2.0 
C) 7.0 
D) 8.0 
A) 9.0 
B) 2.0 
C) 7.0 
D) 8.0

Question 9

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth.
-log x = 2

Accepted Answer

A) 20 
B) 100 
C) 200 
D) 2000 
A) 20 
B) 100 
C) 200 
D) 2000

Question 10

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places.
-0.00502

Accepted Answer

A) -5.2943 
B) -2.2907 
C) -2.3080 
D) -2.2993 
A) -5.2943 
B) -2.2907 
C) -2.3080 
D) -2.2993

Question 11

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth.
-$$\log _ { 2 } 5 x + \log _ { 2 } x = 3$$

Accepted Answer

A) 1.73 
B) 0.77 
C) 1.10 
D) 1.26 
A) 1.73 
B) 0.77 
C) 1.10 
D) 1.26

Question 12

Find the value obtained when 10 is raised to the given exponent. Round to three significant digits.
--2.0891

Accepted Answer

A) -123 
B) 123 
C) 0.00815 
D) -0.00815 
A) -123 
B) 123 
C) 0.00815 
D) -0.00815

Question 13

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth.
-$$\log _ { 125 } x = \frac { 1 } { 3 }$$

Accepted Answer

A)  $\frac { 1 } { 15 }$ 
B) 15 
C)  $\frac { 1 } { 5 }$ 
D) 5 
A)  $\frac { 1 } { 15 }$ 
B) 15 
C)  $\frac { 1 } { 5 }$ 
D) 5

Question 14

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth.
-$$\log _ { 2 } ( - 8 - 3 x ) = 2$$

Accepted Answer

A)  $- \frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 4 }$ 
C) -4 
D) 4 
A)  $- \frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 4 }$ 
C) -4 
D) 4

Question 15

Find the unknown value.
-$\log _ { 5 } 625 = y$

Accepted Answer

A) 20 
B) 5 
C) 4 
D) 625 
A) 20 
B) 5 
C) 4 
D) 625

Question 16

Solve the problem.
-The function $\mathrm { A } = \mathrm { A } _ { \mathrm { o } } \mathrm { e } ^ { - 0.00866 \mathrm { t } }$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where t is the number of years since the material was put into the vault. If 500 pounds of the
Material are initially put into the vault, how many pounds will be left after 150 years? Round to the nearest
Pound.

Accepted Answer

A) 345 lb 
B) 133 lb 
C) 136 lb 
D) 469 lb 
A) 345 lb 
B) 133 lb 
C) 136 lb 
D) 469 lb

Question 17

Solve the problem.
-The value V of a car that is t years old can be modeled by V(t)= 19,518(0.82)t. According to the model, when will the car be worth $6000? Round to the nearest tenth of a year.

Accepted Answer

A) 0.9 yr 
B) 51.1 yr 
C) 5.9 yr 
D) 1.9 yr 
A) 0.9 yr 
B) 51.1 yr 
C) 5.9 yr 
D) 1.9 yr

Question 18

Evaluate.
-$\log _ { 10 } \frac { 1 } { 1000 }$

Accepted Answer

A) 3 
B) 30 
C) -3 
D)  $\frac { 1 } { 1000 }$ 
A) 3 
B) 30 
C) -3 
D)  $\frac { 1 } { 1000 }$

Question 19

Evaluate.
-$\log _ { 12 } 1$

Accepted Answer

A) -12 
B) 12 
C) 0 
D)  $\frac { 1 } { 12 }$ 
A) -12 
B) 12 
C) 0 
D)  $\frac { 1 } { 12 }$

Question 20

Solve the problem.
-The long jump record, in feet, at a particular school can be modeled by f(x)= 20.2 + 2.2 ln (x + 1)where x is the number of years since records began to be kept at the school. What is the record for the long jump 17 years after
Records started being kept? Round your answer to the nearest tenth.

Accepted Answer

A) 22.4 ft 
B) 26.3 ft 
C) 26.6 ft 
D) 26.4 ft 
A) 22.4 ft 
B) 26.3 ft 
C) 26.6 ft 
D) 26.4 ft

Solve the equation. - $\log _ { 3 } ( x - 1 ) + \log _ { 3 } ( x - 7 ) = 3$

Use the change of base formula to find the value of the following logarithm. Do not round logarithms in the change of base formula. Write the answer rounded to the nearest ten-thousandth. - $\log _ { 4 } 0.069$

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places. -3.26

Find the common logarithm of the number. Round answer to four decimal places. -log 0.00281

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. - $f ( x ) = x ^ { 2 } - 7$

Find the number N. Round N to six decimal places. -log N = 2.5224

Write as a logarithm of a single expression. - $\log _ { 6 } ( x + 2 ) - \log _ { 6 } ( x + 7 )$

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. -log x = 2

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places. -0.00502

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - $\log _ { 2 } 5 x + \log _ { 2 } x = 3$

Find the value obtained when 10 is raised to the given exponent. Round to three significant digits. --2.0891

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - $\log _ { 125 } x = \frac { 1 } { 3 }$

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - $\log _ { 2 } ( - 8 - 3 x ) = 2$

Find the unknown value. - $\log _ { 5 } 625 = y$

Solve the problem. -The value V of a car that is t years old can be modeled by V(t)= 19,518(0.82)t. According to the model, when will the car be worth $6000? Round to the nearest tenth of a year.

Evaluate. - $\log _ { 10 } \frac { 1 } { 1000 }$

Evaluate. - $\log _ { 12 } 1$

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

Solve the equation. - log⁡3(x−1)+log⁡3(x−7)=3\log _ { 3 } ( x - 1 ) + \log _ { 3 } ( x - 7 ) = 3log3​(x−1)+log3​(x−7)=3

Use the change of base formula to find the value of the following logarithm. Do not round logarithms in the change of base formula. Write the answer rounded to the nearest ten-thousandth. - log⁡40.069\log _ { 4 } 0.069log4​0.069