Question 1

Write the equation in its equivalent logarithmic form.
-$3 ^ { - 3 } = \frac { 1 } { 27 }$

Accepted Answer

A)  $\log _ { 3 } \frac { 1 } { 27 } = - 3$ 
B)  $\log _ { 1 / 3 } 3 = - 3$ 
C)  $\log _ { 3 } - 3 = \frac { 1 } { 27 }$ 
D)  $\log _ { - 3 } \frac { 1 } { 27 } = 3$ 
A)  $\log _ { 3 } \frac { 1 } { 27 } = - 3$ 
B)  $\log _ { 1 / 3 } 3 = - 3$ 
C)  $\log _ { 3 } - 3 = \frac { 1 } { 27 }$ 
D)  $\log _ { - 3 } \frac { 1 } { 27 } = 3$

Question 2

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { a } \left( \frac { x ^ { 4 } \sqrt [ 3 ] { x + 5 } } { ( x - 2 ) ^ { 2 } } \right)$

Accepted Answer

A)  $\log _ { a } x ^ { 4 } + \log _ { a } ( x + 5 ) ^ { 1 / 3 } - \log _ { a } ( x - 2 ) ^ { 2 }$ 
B)  $4 \log _ { a } x + \frac { 1 } { 3 } \log _ { a } ( x + 5 ) - 2 \log _ { a } ( x - 2 )$ 
C)  $\log _ { a } x ^ { 4 } + \log _ { a } ( x + 5 ) ^ { - 3 } - \log _ { a } ( x - 2 ) ^ { 2 }$ 
D)  $4 \log _ { a } x - 3 \log _ { a } ( x + 5 ) - 2 \log _ { a } ( x - 2 )$ 
A)  $\log _ { a } x ^ { 4 } + \log _ { a } ( x + 5 ) ^ { 1 / 3 } - \log _ { a } ( x - 2 ) ^ { 2 }$ 
B)  $4 \log _ { a } x + \frac { 1 } { 3 } \log _ { a } ( x + 5 ) - 2 \log _ { a } ( x - 2 )$ 
C)  $\log _ { a } x ^ { 4 } + \log _ { a } ( x + 5 ) ^ { - 3 } - \log _ { a } ( x - 2 ) ^ { 2 }$ 
D)  $4 \log _ { a } x - 3 \log _ { a } ( x + 5 ) - 2 \log _ { a } ( x - 2 )$

Question 3

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 8 } \sqrt [ 3 ] { y }$

Accepted Answer

A)  $\frac { 1 } { 3 } \log _ { 8 } y$ 
B)  $3 \log _ { 8 } \mathrm { y }$ 
C)  $\frac { 1 } { 3 } \log _ { 8 } \sqrt [ 3 ] { \mathrm { y } }$ 
D)  $\frac { 1 } { 8 } \log _ { 3 } \mathrm { y }$ 
A)  $\frac { 1 } { 3 } \log _ { 8 } y$ 
B)  $3 \log _ { 8 } \mathrm { y }$ 
C)  $\frac { 1 } { 3 } \log _ { 8 } \sqrt [ 3 ] { \mathrm { y } }$ 
D)  $\frac { 1 } { 8 } \log _ { 3 } \mathrm { y }$

Question 4

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { b } \left( \frac { x y ^ { 7 } } { z ^ { 2 } } \right)$

Accepted Answer

A)  $\log _ { \mathrm { b } } \mathrm { x } + 7 \log _ { \mathrm { b } } \mathrm { y } - 2 \log _ { \mathrm { b } } \mathrm { z }$ 
B)  $\log _ { \mathrm { b } } \mathrm { x } + \log _ { \mathrm { b } } \mathrm { y } ^ { 7 } - \log _ { \mathrm { b } } \mathrm { z } ^ { 2 }$ 
C)  $\log _ { \mathrm { b } } \mathrm { x } + \log _ { \mathrm { b } } \mathrm { y } ^ { 7 } + \log _ { \mathrm { b } ^ { \mathrm { z } } } 2$ 
D)  $\log _ { \mathrm { b } } \mathrm { x } + 7 \log _ { \mathrm { b } } \mathrm { y } + 2 \log _ { \mathrm { b } } \mathrm { z }$ 
A)  $\log _ { \mathrm { b } } \mathrm { x } + 7 \log _ { \mathrm { b } } \mathrm { y } - 2 \log _ { \mathrm { b } } \mathrm { z }$ 
B)  $\log _ { \mathrm { b } } \mathrm { x } + \log _ { \mathrm { b } } \mathrm { y } ^ { 7 } - \log _ { \mathrm { b } } \mathrm { z } ^ { 2 }$ 
C)  $\log _ { \mathrm { b } } \mathrm { x } + \log _ { \mathrm { b } } \mathrm { y } ^ { 7 } + \log _ { \mathrm { b } ^ { \mathrm { z } } } 2$ 
D)  $\log _ { \mathrm { b } } \mathrm { x } + 7 \log _ { \mathrm { b } } \mathrm { y } + 2 \log _ { \mathrm { b } } \mathrm { z }$

Question 5

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 6 } \left( \frac { 7 \cdot 11 } { 13 } \right)$

Accepted Answer

A)  $\log _ { 6 } 5$ 
B)  $\log _ { 6 } 77 - \log _ { 6 } 13$ 
C)  $\log _ { 6 } 7 + \log _ { 6 } 11 - \log _ { 6 } 13$ 
D)  $\log _ { 6 } \left( \frac { 77 } { 13 } \right)$ 
A)  $\log _ { 6 } 5$ 
B)  $\log _ { 6 } 77 - \log _ { 6 } 13$ 
C)  $\log _ { 6 } 7 + \log _ { 6 } 11 - \log _ { 6 } 13$ 
D)  $\log _ { 6 } \left( \frac { 77 } { 13 } \right)$

Question 6

Evaluate or simplify the expression without using a calculator.
-log 1000

Accepted Answer

A)  30 
B)  $\frac { 3 } { 10 }$ 
C)  3 
D)  $\frac { 1 } { 3 }$ 
A)  30 
B)  $\frac { 3 } { 10 }$ 
C)  3 
D)  $\frac { 1 } { 3 }$

Write the equation in its equivalent logarithmic form. - $3 ^ { - 3 } = \frac { 1 } { 27 }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { a } \left( \frac { x ^ { 4 } \sqrt [ 3 ] { x + 5 } } { ( x - 2 ) ^ { 2 } } \right)$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 8 } \sqrt [ 3 ] { y }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { b } \left( \frac { x y ^ { 7 } } { z ^ { 2 } } \right)$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 6 } \left( \frac { 7 \cdot 11 } { 13 } \right)$

Evaluate or simplify the expression without using a calculator. -log 1000

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Exam 4: Exponential and Logarithmic Functions

Write the equation in its equivalent logarithmic form. - 3−3=1273 ^ { - 3 } = \frac { 1 } { 27 }3−3=271​

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡8y3\log _ { 8 } \sqrt [ 3 ] { y }log8​3y​

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡b(xy7z2)\log _ { b } \left( \frac { x y ^ { 7 } } { z ^ { 2 } } \right)logb​(z2xy7​)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡6(7⋅1113)\log _ { 6 } \left( \frac { 7 \cdot 11 } { 13 } \right)log6​(137⋅11​)