Question 1

Change to logarithmic form. $10 ^ { 2 } = 100$

Accepted Answer

A)  log 100 = 3 
B)  ln 100 = 2 
C)  ln 100 = 3 
D)  log 100 = 2 
E)  log 2 = 200 
A)  log 100 = 3 
B)  ln 100 = 2 
C)  ln 100 = 3 
D)  log 100 = 2 
E)  log 2 = 200

Question 2

Solve the equation without using a calculator. $\log \left( x ^ { 7 } \right) = ( \log x ) ^ { 2 }$

Accepted Answer

A)  1 and 10 
B)  2 and 1,000,000 
C)  1,000,000 
D)  1 and 10,000,000 
E)  10,000,000 
A)  1 and 10 
B)  2 and 1,000,000 
C)  1,000,000 
D)  1 and 10,000,000 
E)  10,000,000

Question 3

Write the expression as one logarithm. $\log _ { 3 } ( 8 z ) - \log _ { 3 } ( x )$

Accepted Answer

A)  $\log _ { 3 } \left( \frac { 8 z } { x } \right)$ 
B)  $\log _ { 3 } ( 8 z x )$ 
C)  $\log _ { 3 } \left( \frac { x } { 8 z } \right)$ 
D)  $\log _ { 3 } \left( 8 z - \frac { 1 } { x } \right)$ 
E)  $\log _ { 3 } ( 8 z - x )$ 
A)  $\log _ { 3 } \left( \frac { 8 z } { x } \right)$ 
B)  $\log _ { 3 } ( 8 z x )$ 
C)  $\log _ { 3 } \left( \frac { x } { 8 z } \right)$ 
D)  $\log _ { 3 } \left( 8 z - \frac { 1 } { x } \right)$ 
E)  $\log _ { 3 } ( 8 z - x )$

Question 4

Use common logarithms to solve for x in terms of y. $y = \frac { e ^ { x } - e ^ { - x } } { e ^ { x } + e ^ { - x } }$

Accepted Answer

A)  $x = 3 \ln \frac { y - 1 } { y + 1 }$ 
B)  $x = \frac { 1 } { 2 } \ln \frac { y + 1 } { 1 - y }$ 
C)  $x = 2 \ln \frac { y - 1 } { y + 1 }$ 
D)  $x = \frac { 1 } { 3 } \ln \frac { y + 1 } { y - 1 }$ 
E)  $x = \ln \frac { y - 1 } { y + 1 }$ 
A)  $x = 3 \ln \frac { y - 1 } { y + 1 }$ 
B)  $x = \frac { 1 } { 2 } \ln \frac { y + 1 } { 1 - y }$ 
C)  $x = 2 \ln \frac { y - 1 } { y + 1 }$ 
D)  $x = \frac { 1 } { 3 } \ln \frac { y + 1 } { y - 1 }$ 
E)  $x = \ln \frac { y - 1 } { y + 1 }$

Change to logarithmic form. $10 ^ { 2 } = 100$

Solve the equation without using a calculator. $\log \left( x ^ { 7 } \right) = ( \log x ) ^ { 2 }$

Write the expression as one logarithm. $\log _ { 3 } ( 8 z ) - \log _ { 3 } ( x )$

Use common logarithms to solve for x in terms of y. $y = \frac { e ^ { x } - e ^ { - x } } { e ^ { x } + e ^ { - x } }$

Topics From Algebra

Functions and Graphs

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series, and Probability

Topics From Analytical Geometry

Filters

Exam 4: Inverse, Exponential, and Logarithmic Functions

Change to logarithmic form. 102=10010 ^ { 2 } = 100102=100

Solve the equation without using a calculator. log⁡(x7)=(log⁡x)2\log \left( x ^ { 7 } \right) = ( \log x ) ^ { 2 }log(x7)=(logx)2

Write the expression as one logarithm. log⁡3(8z)−log⁡3(x)\log _ { 3 } ( 8 z ) - \log _ { 3 } ( x )log3​(8z)−log3​(x)

Use common logarithms to solve for x in terms of y. y=ex−e−xex+e−xy = \frac { e ^ { x } - e ^ { - x } } { e ^ { x } + e ^ { - x } }y=ex+e−xex−e−x​

Topics From Algebra

Functions and Graphs

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series, and Probability

Topics From Analytical Geometry

Filters

Change to logarithmic form. $10 ^ { 2 } = 100$

Solve the equation without using a calculator. $\log \left( x ^ { 7 } \right) = ( \log x ) ^ { 2 }$

Write the expression as one logarithm. $\log _ { 3 } ( 8 z ) - \log _ { 3 } ( x )$

Use common logarithms to solve for x in terms of y. $y = \frac { e ^ { x } - e ^ { - x } } { e ^ { x } + e ^ { - x } }$