Question 1

Identify the vertical asymptote of $g ( t ) = - 6 + \log _ { 7 } t$.

Accepted Answer

A)   t=-6 
B)   t=6 
C)   t=7 
D)   t=-7 
E) y -axis 
A)   t=-6 
B)   t=6 
C)   t=7 
D)   t=-7 
E) y -axis

Question 2

Match the graph with the graph of its inverse function.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 3

Find $( g \circ f ) ( 3 )$ where $f ( x ) = 5 x + 2$ and $g ( x ) = x - 5$ .

Accepted Answer

A) 12 
B) 15 
C) -28 
D) -8 
E) -34 
A) 12 
B) 15 
C) -28 
D) -8 
E) -34

Question 4

Solve the logarithmic equation. Round your answer to two decimal places. $$\log _ { 2 } ( x - 1 ) + \log _ { 2 } ( x + 2 ) = 3$$

Accepted Answer

A)  $x = 9.00$ 
B)  $x = 2.70$ 
C)  $x = 3.50$ 
D)  $x = 0.14$ 
E)  $x = - 3.70$ 
A)  $x = 9.00$ 
B)  $x = 2.70$ 
C)  $x = 3.50$ 
D)  $x = 0.14$ 
E)  $x = - 3.70$

Question 5

Use the properties of logarithms to condense $6 \log _ { 10 } ( x + y ) + 4 \log _ { 10 } w$ .

Accepted Answer

A)  $\log _ { 10 } x ^ { 6 } y ^ { 6 } w ^ { 4 }$ 
B)  $\log _ { 10 } \left( x ^ { 6 } + y ^ { 6 } \right) w ^ { 4 }$ 
C)  $\log _ { 10 } ( 6 ( x + y ) + 4 w )$ 
D)  $\log _ { 10 } 24 ( x + y ) w$ 
E)  $\log _ { 10 } ( x + y ) ^ { 6 } w ^ { 4 }$ 
A)  $\log _ { 10 } x ^ { 6 } y ^ { 6 } w ^ { 4 }$ 
B)  $\log _ { 10 } \left( x ^ { 6 } + y ^ { 6 } \right) w ^ { 4 }$ 
C)  $\log _ { 10 } ( 6 ( x + y ) + 4 w )$ 
D)  $\log _ { 10 } 24 ( x + y ) w$ 
E)  $\log _ { 10 } ( x + y ) ^ { 6 } w ^ { 4 }$

Question 6

An investment is made in an account that pays 6.25%, compounded continuously. What is the effective yield for this investment? Round your answer to two decimal places.

Accepted Answer

A) 6.25% 
B) 6.40% 
C) 6.94% 
D) 6.45% 
E) 6.35% 
A) 6.25% 
B) 6.40% 
C) 6.94% 
D) 6.45% 
E) 6.35%

Question 7

Evaluate the function as indicated. Round your answer to three decimal places. $\begin{aligned}
G ( x ) & = 1.7 ^ { - x } \
x & = - 1
\end{aligned}$

Accepted Answer

A) -0.588 
B) 0.588 
C) 2.700 
D) 1.700 
E) -1.700 
A) -0.588 
B) 0.588 
C) 2.700 
D) 1.700 
E) -1.700

Question 8

Find $( f \circ g ) ( - 3 )$ where $f ( x ) = 4 x + 6$ and $g ( x ) = x ^ { 2 } - 4$ .

Accepted Answer

A) 32 
B) 38 
C) 146 
D) 132 
E) 26 
A) 32 
B) 38 
C) 146 
D) 132 
E) 26

Question 9

The population of a region for 2000 is 19.5 (in millions). The predicted population (in millions)for the region in the year 2020 is 24. Find the constants C (to one decimal place)and k (to four decimal places)to obtain the experimental growth model $y = C e ^ { k t }$ for the population. (Let $t = 0$ correspond to the year 2000.)

Accepted Answer

A)  $y = 19.5 e ^ { 0.0045 t }$ 
B)  $y = 7.2 e ^ { 1.2076 t }$ 
C)  $y = 19.5 e ^ { 0.2076 t }$ 
D)  $y = 19.5 e ^ { 0.0104 t }$ 
E)  $y = 7.2 e ^ { 0.0604 t }$ 
A)  $y = 19.5 e ^ { 0.0045 t }$ 
B)  $y = 7.2 e ^ { 1.2076 t }$ 
C)  $y = 19.5 e ^ { 0.2076 t }$ 
D)  $y = 19.5 e ^ { 0.0104 t }$ 
E)  $y = 7.2 e ^ { 0.0604 t }$

Question 10

Use the properties of logarithms to evaluate $\ln e ^ { 15 } + \ln e ^ { 3 }$ without a calculator.

Accepted Answer

A) 0 
B) 5 
C)  $14.81$ 
D)  $10.27$ 
E) 12 
A) 0 
B) 5 
C)  $14.81$ 
D)  $10.27$ 
E) 12

Question 11

Match the graph with the graph of its inverse function.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Determine whether the value x=729 is a solution of the equation $\log _ { 9 } ( 7 x ) = \frac { 3 } { 2 }$ .

Accepted Answer

A) not a solution 
B) solution 
A) not a solution 
B) solution

Question 13

Evaluate the function as indicated. Round your answer to three decimal places. $\begin{aligned}
g ( x ) & = 100 e ^ { - 0.5 x } \
x & = 8
\end{aligned}$

Accepted Answer

A) -1087.313 
B) 1.832 
C) 5459.815 
D) 1.593 
E) -485.225 
A) -1087.313 
B) 1.832 
C) 5459.815 
D) 1.593 
E) -485.225

Question 14

Simplify the expression. $- 5 e ^ { - 6 x }$

Accepted Answer

A)  $5 e ^ { 6 x }$ 
B)  $- \frac { 5 } { e ^ { 6 x } }$ 
C)  $- 5 \sqrt [ 6 x ] { e }$ 
D)  $\frac { 5 } { e ^ { 6 x } }$ 
E)  $\sqrt [ 6 x ] { - 5 e }$ 
A)  $5 e ^ { 6 x }$ 
B)  $- \frac { 5 } { e ^ { 6 x } }$ 
C)  $- 5 \sqrt [ 6 x ] { e }$ 
D)  $\frac { 5 } { e ^ { 6 x } }$ 
E)  $\sqrt [ 6 x ] { - 5 e }$

Question 15

Match $f ( x ) = \log _ { 2 } ( x + 3 )$ with its graph.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Evaluate the function as indicated. Round your answer to three decimal places. $\begin{aligned}
g ( x ) & = 50 e ^ { - 0.1 x } \
x & = - 20
\end{aligned}$

Accepted Answer

A) -6.767 
B) 6.767 
C) -904.837 
D) 369.453 
E) 210.588 
A) -6.767 
B) 6.767 
C) -904.837 
D) 369.453 
E) 210.588

Question 17

Use the properties of logarithms to evaluate $\log _ { 27 } 9 + \log _ { 27 } 81$ without a calculator.

Accepted Answer

A) 2 
B)  $ \frac{2}{3} $ 
C)  $ \frac{3}{4} $ 
D)  4 
E) 1 
A) 2 
B)  $ \frac{2}{3} $ 
C)  $ \frac{3}{4} $ 
D)  4 
E) 1

Question 18

Graph the function $f ( x ) = - \log _ { 2 } ( x - 1 )$ .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

Evaluate the logarithm. $\log _ { 36 } 216$

Accepted Answer

A)  $\frac { 3 } { 2 }$ 
B) 3 
C)  $\frac { 2 } { 3 }$ 
D) 6 
E)  $\log _ { 36 } 216$ is undefined. 
A)  $\frac { 3 } { 2 }$ 
B) 3 
C)  $\frac { 2 } { 3 }$ 
D) 6 
E)  $\log _ { 36 } 216$ is undefined.

Question 20

Solve the equation. Do not use a calculator. $7 ^ { x + 3 } = 49 ^ { 6 }$

Accepted Answer

A)  $x = 1.5$ 
B)  x=3 
C)  x=6 
D)  x=9 
E)  x=15 
A)  $x = 1.5$ 
B)  x=3 
C)  x=6 
D)  x=9 
E)  x=15

Identify the vertical asymptote of $g ( t ) = - 6 + \log _ { 7 } t$ .

Match the graph with the graph of its inverse function.

Find $( g \circ f ) ( 3 )$ where $f ( x ) = 5 x + 2$ and $g ( x ) = x - 5$ .

Solve the logarithmic equation. Round your answer to two decimal places. $\log _ { 2 } ( x - 1 ) + \log _ { 2 } ( x + 2 ) = 3$

Use the properties of logarithms to condense $6 \log _ { 10 } ( x + y ) + 4 \log _ { 10 } w$ .

An investment is made in an account that pays 6.25%, compounded continuously. What is the effective yield for this investment? Round your answer to two decimal places.

Evaluate the function as indicated. Round your answer to three decimal places. G(x) =1. x =-1

Find $( f \circ g ) ( - 3 )$ where $f ( x ) = 4 x + 6$ and $g ( x ) = x ^ { 2 } - 4$ .

Use the properties of logarithms to evaluate $\ln e ^ { 15 } + \ln e ^ { 3 }$ without a calculator.

Match the graph with the graph of its inverse function.

Determine whether the value x=729 is a solution of the equation $\log _ { 9 } ( 7 x ) = \frac { 3 } { 2 }$ .

Evaluate the function as indicated. Round your answer to three decimal places. g(x) =100 x =8

Simplify the expression. $- 5 e ^ { - 6 x }$

Match $f ( x ) = \log _ { 2 } ( x + 3 )$ with its graph.

Evaluate the function as indicated. Round your answer to three decimal places. g(x) =50 x =-20

Use the properties of logarithms to evaluate $\log _ { 27 } 9 + \log _ { 27 } 81$ without a calculator.

Graph the function $f ( x ) = - \log _ { 2 } ( x - 1 )$ .

Evaluate the logarithm. $\log _ { 36 } 216$

Solve the equation. Do not use a calculator. $7 ^ { x + 3 } = 49 ^ { 6 }$

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Conics

Sequences, Series, and the Binomial Theorem

Filters

Exam 9: Exponential and Logarithmic Functions

Identify the vertical asymptote of g(t)=−6+log⁡7tg ( t ) = - 6 + \log _ { 7 } tg(t)=−6+log7​t .

Match the graph with the graph of its inverse function.

Find (g∘f)(3)( g \circ f ) ( 3 )(g∘f)(3) where f(x)=5x+2f ( x ) = 5 x + 2f(x)=5x+2 and g(x)=x−5g ( x ) = x - 5g(x)=x−5 .

Solve the logarithmic equation. Round your answer to two decimal places. log⁡2(x−1)+log⁡2(x+2)=3\log _ { 2 } ( x - 1 ) + \log _ { 2 } ( x + 2 ) = 3log2​(x−1)+log2​(x+2)=3

Use the properties of logarithms to condense 6log⁡10(x+y)+4log⁡10w6 \log _ { 10 } ( x + y ) + 4 \log _ { 10 } w6log10​(x+y)+4log10​w .

An investment is made in an account that pays 6.25%, compounded continuously. What is the effective yield for this investment? Round your answer to two decimal places.

Evaluate the function as indicated. Round your answer to three decimal places. G(x) =1. x =-1

Find (f∘g)(−3)( f \circ g ) ( - 3 )(f∘g)(−3) where f(x)=4x+6f ( x ) = 4 x + 6f(x)=4x+6 and g(x)=x2−4g ( x ) = x ^ { 2 } - 4g(x)=x2−4 .

Use the properties of logarithms to evaluate ln⁡e15+ln⁡e3\ln e ^ { 15 } + \ln e ^ { 3 }lne15+lne3 without a calculator.

Match the graph with the graph of its inverse function.

Determine whether the value x=729 is a solution of the equation log⁡9(7x)=32\log _ { 9 } ( 7 x ) = \frac { 3 } { 2 }log9​(7x)=23​ .

Evaluate the function as indicated. Round your answer to three decimal places. g(x) =100 x =8

Simplify the expression. −5e−6x- 5 e ^ { - 6 x }−5e−6x

Match f(x)=log⁡2(x+3)f ( x ) = \log _ { 2 } ( x + 3 )f(x)=log2​(x+3) with its graph.

Evaluate the function as indicated. Round your answer to three decimal places. g(x) =50 x =-20

Use the properties of logarithms to evaluate log⁡279+log⁡2781\log _ { 27 } 9 + \log _ { 27 } 81log27​9+log27​81 without a calculator.

Graph the function f(x)=−log⁡2(x−1)f ( x ) = - \log _ { 2 } ( x - 1 )f(x)=−log2​(x−1) .

Evaluate the logarithm. log⁡36216\log _ { 36 } 216log36​216

Solve the equation. Do not use a calculator. 7x+3=4967 ^ { x + 3 } = 49 ^ { 6 }7x+3=496

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Conics

Sequences, Series, and the Binomial Theorem

Filters

Identify the vertical asymptote of $g ( t ) = - 6 + \log _ { 7 } t$ .

Find $( g \circ f ) ( 3 )$ where $f ( x ) = 5 x + 2$ and $g ( x ) = x - 5$ .

Solve the logarithmic equation. Round your answer to two decimal places. $\log _ { 2 } ( x - 1 ) + \log _ { 2 } ( x + 2 ) = 3$

Use the properties of logarithms to condense $6 \log _ { 10 } ( x + y ) + 4 \log _ { 10 } w$ .

Find $( f \circ g ) ( - 3 )$ where $f ( x ) = 4 x + 6$ and $g ( x ) = x ^ { 2 } - 4$ .

Use the properties of logarithms to evaluate $\ln e ^ { 15 } + \ln e ^ { 3 }$ without a calculator.

Determine whether the value x=729 is a solution of the equation $\log _ { 9 } ( 7 x ) = \frac { 3 } { 2 }$ .

Simplify the expression. $- 5 e ^ { - 6 x }$

Match $f ( x ) = \log _ { 2 } ( x + 3 )$ with its graph.

Use the properties of logarithms to evaluate $\log _ { 27 } 9 + \log _ { 27 } 81$ without a calculator.

Graph the function $f ( x ) = - \log _ { 2 } ( x - 1 )$ .

Evaluate the logarithm. $\log _ { 36 } 216$

Solve the equation. Do not use a calculator. $7 ^ { x + 3 } = 49 ^ { 6 }$