Question 1

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

Question 2

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​

Accepted Answer

A)    x=3ln⁡y−1y+1x = 3 \ln \frac { y - 1 } { y + 1 }x=3lny+1y−1​ 
B)    x=12ln⁡y+11−yx = \frac { 1 } { 2 } \ln \frac { y + 1 } { 1 - y }x=21​ln1−yy+1​ 
C)    x=2ln⁡y−1y+1x = 2 \ln \frac { y - 1 } { y + 1 }x=2lny+1y−1​ 
D)    x=13ln⁡y+1y−1x = \frac { 1 } { 3 } \ln \frac { y + 1 } { y - 1 }x=31​lny−1y+1​ 
E)    x=ln⁡y−1y+1x = \ln \frac { y - 1 } { y + 1 }x=lny+1y−1​F) A) and B)
G) A) and C)

Question 3

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

Accepted Answer

A)    log⁡3(8zx) \log _ { 3 } \left( \frac { 8 z } { x } \right) log3​(x8z​)  
B)    log⁡3(8zx) \log _ { 3 } ( 8 z x ) log3​(8zx)  
C)    log⁡3(x8z) \log _ { 3 } \left( \frac { x } { 8 z } \right) log3​(8zx​)  
D)    log⁡3(8z−1x) \log _ { 3 } \left( 8 z - \frac { 1 } { x } \right) log3​(8z−x1​)  
E)    log⁡3(8z−x) \log _ { 3 } ( 8 z - x ) log3​(8z−x) F) A) and E)
G) D) and E)

Question 4

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

Accepted Answer

A)   log 100 = 3
B)   ln 100 = 2
C)   ln 100 = 3
D)   log 100 = 2
E)   log 2 = 200 F) C) and E)
G) All of the above

Exam 4: Inverse, Exponential, and Logarithmic Functions

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

Exam 4: Inverse, Exponential, and Logarithmic Functions

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​

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified