Question 1

Evaluate. Round to the nearest thousandth, if necessary.
-$\log \left( \frac { 1 } { 1000 } \right)$

Accepted Answer

A)  100 
B)  $- 3$ 
C)  $- 100$ 
D)  3 
A)  100 
B)  $- 3$ 
C)  $- 100$ 
D)  3

Question 2

Rewrite in logarithmic form.
-$$4 ^ { - 2 } = \frac { 1 } { 16 }$$

Accepted Answer

A)  $\log _ { 1 / 16 } 4 = - 2$ 
B)  $\log _ { 4 } - 2 = \frac { 1 } { 16 }$ 
C)  $\log _ { - 2 } \frac { 1 } { 16 } = 4$ 
D)  $\log _ { 4 } \frac { 1 } { 16 } = - 2$ 
A)  $\log _ { 1 / 16 } 4 = - 2$ 
B)  $\log _ { 4 } - 2 = \frac { 1 } { 16 }$ 
C)  $\log _ { - 2 } \frac { 1 } { 16 } = 4$ 
D)  $\log _ { 4 } \frac { 1 } { 16 } = - 2$

Question 3

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.
-$$f ( x ) = 2 ^ { x + 3 }$$

Accepted Answer

A)  Horizontal asymptote: $y = - 3$;
Domain: $( - \infty , \infty )$, Range: $( - 3 , \infty )$ 
B)  Horizontal asymptote: $\mathrm { y } = 2$;
Domain: $( - \infty , \infty )$, Range: $( 2 , \infty )$ 
C)  Horizontal asymptote: $\mathrm { y } = 0$;
Domain: $( - \infty , \infty )$, Range: $( 0 , \infty )$ 
D)  Horizontal asymptote: $\mathrm { y } = 3$;
Domain: $( - \infty , \infty )$, Range: $( 3 , \infty )$ 
A)  Horizontal asymptote: $y = - 3$;
Domain: $( - \infty , \infty )$, Range: $( - 3 , \infty )$ 
B)  Horizontal asymptote: $\mathrm { y } = 2$;
Domain: $( - \infty , \infty )$, Range: $( 2 , \infty )$ 
C)  Horizontal asymptote: $\mathrm { y } = 0$;
Domain: $( - \infty , \infty )$, Range: $( 0 , \infty )$ 
D)  Horizontal asymptote: $\mathrm { y } = 3$;
Domain: $( - \infty , \infty )$, Range: $( 3 , \infty )$

Question 4

Suppose for some base b > 0 (b ≠ 1) that logb 2 = A, logb 3 = B, logb 5 = C, and logb 7 = D. Express the given logarithms
in terms of A, B, C, or D.
-$\log _ { b } 25$

Accepted Answer

A)  $3 \mathrm { D }$ 
B)  $2 \mathrm { D }$ 
C)  $2 \mathrm { C }$ 
D)  $3 C$ 
A)  $3 \mathrm { D }$ 
B)  $2 \mathrm { D }$ 
C)  $2 \mathrm { C }$ 
D)  $3 C$

Question 5

Compute the compound interest.
-How long will it take for $8900 to grow to $12,400 at an interest rate of 3.5% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

Accepted Answer

A)  3.5 yr 
B)  947.56 yr 
C)  0.95 yr 
D)  9.48 yr 
A)  3.5 yr 
B)  947.56 yr 
C)  0.95 yr 
D)  9.48 yr

Question 6

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables
represent positive real numbers.
-$\log _ { 3 } \left( \frac { x y } { 4 } \right)$

Accepted Answer

A)  $\left( \log _ { 3 } x \right) \left( \log _ { 3 } y \right) \div \log _ { 3 } 4$ 
B)  $\log _ { 3 } x + \log _ { 3 } y + \log _ { 3 } 4$ 
C)  $\log _ { 3 } x + \log _ { 3 } y - \log _ { 3 } 4$ 
D)  $\left( \log _ { 3 } x \right) ^ { 2 } + \left( \log _ { 3 } y \right) ^ { 2 } - \log _ { 3 } 4$ 
A)  $\left( \log _ { 3 } x \right) \left( \log _ { 3 } y \right) \div \log _ { 3 } 4$ 
B)  $\log _ { 3 } x + \log _ { 3 } y + \log _ { 3 } 4$ 
C)  $\log _ { 3 } x + \log _ { 3 } y - \log _ { 3 } 4$ 
D)  $\left( \log _ { 3 } x \right) ^ { 2 } + \left( \log _ { 3 } y \right) ^ { 2 } - \log _ { 3 } 4$

Question 7

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real
numbers.
-$$\log _ { x } 35 - \log _ { x } 7$$

Accepted Answer

A)  $\frac { \log _ { x } 35 } { \log _ { x } 7 }$ 
B)  $\log _ { x } 245$ 
C)  $\log _ { x } 5$ 
D)  $\log _ { x } 28$ 
A)  $\frac { \log _ { x } 35 } { \log _ { x } 7 }$ 
B)  $\log _ { x } 245$ 
C)  $\log _ { x } 5$ 
D)  $\log _ { x } 28$

Question 8

Evaluate. Round to the nearest thousandth, if necessary.
-$\log 242$

Accepted Answer

A)  $2.382$ 
B)  $2.384$ 
C)  $2.386$ 
D)  $5.489$ 
A)  $2.382$ 
B)  $2.384$ 
C)  $2.386$ 
D)  $5.489$

Question 9

Evaluate the given function.
-$f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x + 2 } + 7 , f ( 1 )$

Accepted Answer

A)  $7 \frac { 1 } { 2187 }$ 
B)  $7 \frac { 1 } { 9 }$ 
C)  $7 \frac { 1 } { 27 }$ 
D)  $10 \frac { 1 } { 27 }$ 
A)  $7 \frac { 1 } { 2187 }$ 
B)  $7 \frac { 1 } { 9 }$ 
C)  $7 \frac { 1 } { 27 }$ 
D)  $10 \frac { 1 } { 27 }$

Question 10

Simplify.
-$\log 10 ^ { 33 }$

Accepted Answer

A)  0 
B)  1 
C)  $- 33$ 
D)  33 
A)  0 
B)  1 
C)  $- 33$ 
D)  33

Question 11

Rewrite in logarithmic form.
-$$4 ^ { 3 } = 64$$

Accepted Answer

A)  $\log _ { 64 } 4 = 3$ 
B)  $\log _ { 4 } 3 = 64$ 
C)  $\log _ { 4 } 64 = 3$ 
D)  $\log _ { 3 } 64 = 4$ 
A)  $\log _ { 64 } 4 = 3$ 
B)  $\log _ { 4 } 3 = 64$ 
C)  $\log _ { 4 } 64 = 3$ 
D)  $\log _ { 3 } 64 = 4$

Question 12

Evaluate the given function.    
-$$f ( x ) = \log _ { 6 } x , f ( 1 )$$

Accepted Answer

A)  1 
B)  6 
C)  $- 6$ 
D)  0 
A)  1 
B)  6 
C)  $- 6$ 
D)  0

Question 13

Rewrite using the power rule. Assume all variables represent positive real numbers.
-$$\log _ { 3 } \sqrt [ 6 ] { z }$$

Accepted Answer

A)  $6 \log _ { 3 } z$ 
B)  $\log _ { 3 } \frac { z } { 6 }$ 
C)  $\frac { 1 } { 6 } \log _ { 3 } z$ 
D)  $\frac { 1 } { 2 } \log z$ 
A)  $6 \log _ { 3 } z$ 
B)  $\log _ { 3 } \frac { z } { 6 }$ 
C)  $\frac { 1 } { 6 } \log _ { 3 } z$ 
D)  $\frac { 1 } { 2 } \log z$

Question 14

Solve the problem.
-The space in a landfill (in acres) decreases with time as given by the function $F ( t ) = 300 - 50 \log _ { 5 } ( 4 t + 1 )$, where $t$ is measured in years. How much space is left when $t = 6$ ?

Accepted Answer

A)  220 acres 
B)  200 acres 
C)  400 acres 
D)  110 acres 
A)  220 acres 
B)  200 acres 
C)  400 acres 
D)  110 acres

Evaluate. Round to the nearest thousandth, if necessary. - $\log \left( \frac { 1 } { 1000 } \right)$

Rewrite in logarithmic form. - $4 ^ { - 2 } = \frac { 1 } { 16 }$

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - $f ( x ) = 2 ^ { x + 3 }$

Suppose for some base b > 0 (b ≠ 1) that logb 2 = A, logb 3 = B, logb 5 = C, and logb 7 = D. Express the given logarithms in terms of A, B, C, or D. - $\log _ { b } 25$

Compute the compound interest. -How long will it take for $8900 to grow to $12,400 at an interest rate of 3.5% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers. - $\log _ { 3 } \left( \frac { x y } { 4 } \right)$

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { x } 35 - \log _ { x } 7$

Evaluate. Round to the nearest thousandth, if necessary. - $\log 242$

Evaluate the given function. - $f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x + 2 } + 7 , f ( 1 )$

Simplify. - $\log 10 ^ { 33 }$

Rewrite in logarithmic form. - $4 ^ { 3 } = 64$

Evaluate the given function. $Evaluate the given function. - f ( x ) = \log _ { 6 } x , f ( 1 )$ $Evaluate the given function. - f ( x ) = \log _ { 6 } x , f ( 1 )$ - $f ( x ) = \log _ { 6 } x , f ( 1 )$

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log _ { 3 } \sqrt [ 6 ] { z }$

Solve the problem. -The space in a landfill (in acres) decreases with time as given by the function $F ( t ) = 300 - 50 \log _ { 5 } ( 4 t + 1 )$ , where $t$ is measured in years. How much space is left when $t = 6$ ?

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 12: Logarithmic and Exponential Functions

Evaluate. Round to the nearest thousandth, if necessary. - log⁡(11000)\log \left( \frac { 1 } { 1000 } \right)log(10001​)

Rewrite in logarithmic form. - 4−2=1164 ^ { - 2 } = \frac { 1 } { 16 }4−2=161​

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - f(x)=2x+3f ( x ) = 2 ^ { x + 3 }f(x)=2x+3

Suppose for some base b > 0 (b ≠ 1) that logb 2 = A, logb 3 = B, logb 5 = C, and logb 7 = D. Express the given logarithms in terms of A, B, C, or D. - log⁡b25\log _ { b } 25logb​25