Question 1

Use the properties of logarithms to condense $4 \ln 3 - 3 \ln x - \ln y$ .

Accepted Answer

A)  $\ln \left( 81 - x ^ { 3 } - y \right)$ 
B)  $\ln \frac { 12 x ^ { 3 } } { y }$ 
C)  $\ln \frac { 81 x ^ { 3 } } { y }$ 
D)  $\ln ( 12 - 3 x - y )$ 
E)  $\ln \frac { 81 } { x ^ { 3 } y }$ 
A)  $\ln \left( 81 - x ^ { 3 } - y \right)$ 
B)  $\ln \frac { 12 x ^ { 3 } } { y }$ 
C)  $\ln \frac { 81 x ^ { 3 } } { y }$ 
D)  $\ln ( 12 - 3 x - y )$ 
E)  $\ln \frac { 81 } { x ^ { 3 } y }$

Question 2

Solve the equation. Do not use a calculator. $$4 ^ { x + 6 } = \frac { 1 } { 16 }$$

Accepted Answer

A)  $x = 2$ 
B)  $x = 8$ 
C)  $x = - 5 \frac { 15 } { 16 }$ 
D)  $x = - 8$ 
E)  $x = - 5 \frac { 1 } { 2 }$ 
A)  $x = 2$ 
B)  $x = 8$ 
C)  $x = - 5 \frac { 15 } { 16 }$ 
D)  $x = - 8$ 
E)  $x = - 5 \frac { 1 } { 2 }$

Question 3

Students participating in an experiment attended several lectures on a subject. Every month for a year after that, the students were tested to see how much of the material they remembered. The average scores for the group are given by the human memory model $f ( t ) = 80 - \log _ { 10 } ( t + 1 ) ^ { 12 } , 0 \leq t \leq 12$ where t is the time in months. Find the average score for the group after 11 months. Round your answer to three decimal places.

Accepted Answer

A)  $67.05$ 
B)  $67.503$ 
C)  $78.921$ 
D)  $77.505$ 
E)  $78.373$ 
A)  $67.05$ 
B)  $67.503$ 
C)  $78.921$ 
D)  $77.505$ 
E)  $78.373$

Question 4

Solve the logarithmic equation. Round your answer to two decimal places. $3 \log _ { 6 } x = 27$

Accepted Answer

A)  $x = 531,441.00$ 
B)  $x = 1.22$ 
C)  $x = 1.23$ 
D)  $x = 10,077,696.00$ 
E)  $x = 8.00$ 
A)  $x = 531,441.00$ 
B)  $x = 1.22$ 
C)  $x = 1.23$ 
D)  $x = 10,077,696.00$ 
E)  $x = 8.00$

Question 5

Evaluate the expression $6 ^ { \sqrt { 2 } }$ . Round your answer to three decimal places.

Accepted Answer

A) 8.485 
B) 3.000 
C) 12.603 
D) 2.449 
E) 22.274 
A) 8.485 
B) 3.000 
C) 12.603 
D) 2.449 
E) 22.274

Question 6

Simplify the expression $\log _ { 6 } 6 ^ { x ^ { 8 } }$ .

Accepted Answer

A)  $x ^ { 8 }$ 
B)  $8 x ^ { 8 }$ 
C)  $6 x ^ { 8 }$ 
D)  $x ^ { 6 }$ 
E)  $8 x ^ { 9 }$ 
A)  $x ^ { 8 }$ 
B)  $8 x ^ { 8 }$ 
C)  $6 x ^ { 8 }$ 
D)  $x ^ { 6 }$ 
E)  $8 x ^ { 9 }$

Question 7

Match $f ( x ) = - 3 ^ { x }$ with its graph.

Accepted Answer

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

Question 8

Determine the balance A ( to the nearest cent)for P=500 dollars invested at a rate r=7% for t=10 , compounded 12 times per year. Round the answer to two decimal places.

Accepted Answer

A) $529.94 
B) $4,700.00 
C) $1,126.10 
D) $1,004.83 
E) $6,359.33 
A) $529.94 
B) $4,700.00 
C) $1,126.10 
D) $1,004.83 
E) $6,359.33

Question 9

Determine the balance A ( to the nearest cent)for P=3,000 dollars invested at a rate r=10% for t=10 , compounded one time per year. Round the answer to two decimal places.

Accepted Answer

A) $33,000.00 
B) $4,781.23 
C) $3,000.00 
D) $6,000.00 
E) $7,781.23 
A) $33,000.00 
B) $4,781.23 
C) $3,000.00 
D) $6,000.00 
E) $7,781.23

Question 10

Identify the vertical asymptote of $g ( x ) = \log _ { 10 } ( x - 1 )$ .

Accepted Answer

A)  x=10 
B)  x=1 
C)  x=-1 
D) y -axis 
E)  x=5 
A)  x=10 
B)  x=1 
C)  x=-1 
D) y -axis 
E)  x=5

Question 11

Evaluate the function as indicated. Round to three decimal places if necessary.

$\begin{array}{c}
 10,000 ( 1.09 ) ^ { 3 t }\
t = 5.5
\end{array}$

Accepted Answer

A) 212,352.559 
B) 227981.657 
C) 16,063.706 
D) 41,451.210 
E) 179,850.000 
A) 212,352.559 
B) 227981.657 
C) 16,063.706 
D) 41,451.210 
E) 179,850.000

Question 12

An investment is made in an account that pays 9.25%, compounded daily. What is the effective yield for this investment? Round your answer to two decimal places.

Accepted Answer

A) 9.69% 
B) 9.46% 
C) 9.65% 
D) 9.58% 
E) 9.25% 
A) 9.69% 
B) 9.46% 
C) 9.65% 
D) 9.58% 
E) 9.25%

Question 13

Solve the equation. Do not use a calculator. $$\log _ { 6 } ( 2 x + 9 ) = \log _ { 6 } ( 4 x + 5 )$$

Accepted Answer

A)  $x = 2$ 
B)  $x = - 7$ 
C)  $x = 7$ 
D)  $x = - 2$ 
E) no solution 
A)  $x = 2$ 
B)  $x = - 7$ 
C)  $x = 7$ 
D)  $x = - 2$ 
E) no solution

Question 14

Use the properties of logarithms to condense $6 \log _ { 10 } x - 4 \log _ { 10 } 2$ .

Accepted Answer

A)  $\log _ { 10 } ( x - z ) ^ { 2 }$ 
B)  $\log _ { 10 } x ^ { 4 } - \log _ { 10 } z ^ { 4 }$ 
C)  $\log _ { 10 } \frac { 6 x } { 4 z }$ 
D)  $\log _ { 10 } \frac { x ^ { 6 } } { z ^ { 4 } }$ 
E)  $\log _ { 10 } ( 6 x - 4 z )$ 
A)  $\log _ { 10 } ( x - z ) ^ { 2 }$ 
B)  $\log _ { 10 } x ^ { 4 } - \log _ { 10 } z ^ { 4 }$ 
C)  $\log _ { 10 } \frac { 6 x } { 4 z }$ 
D)  $\log _ { 10 } \frac { x ^ { 6 } } { z ^ { 4 } }$ 
E)  $\log _ { 10 } ( 6 x - 4 z )$

Question 15

Find $( g \circ f ) ( x )$ where $f ( x ) = 4 x + 7$ and $g ( x ) = x ^ { 2 } - 1$ .

Accepted Answer

A)  $4 x ^ { 3 } 28 x ^ { 2 } - 4 x - 7$ 
B)  $4 x ^ { 2 } + 3$ 
C)  $16 x ^ { 2 } + 56 x + 48$ 
D)  $16 x ^ { 2 } + 6$ 
E)  $4 x ^ { 2 } + 6$ 
A)  $4 x ^ { 3 } 28 x ^ { 2 } - 4 x - 7$ 
B)  $4 x ^ { 2 } + 3$ 
C)  $16 x ^ { 2 } + 56 x + 48$ 
D)  $16 x ^ { 2 } + 6$ 
E)  $4 x ^ { 2 } + 6$

Question 16

Graph the function $\ln ( x ) = 2 \ln ( x + 3 )$ .

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 17

Use $\ln 4 \approx 1.3863$ , $\ln 14 \approx 2.6391$ , and the properties of logarithms to approximate $\ln 56$ to four decimal places.

Accepted Answer

A)  $4.0254$ 
B)  $3.6585$ 
C)  $19.4081$ 
D)  $1.9037$ 
E)  $10.5562$ 
A)  $4.0254$ 
B)  $3.6585$ 
C)  $19.4081$ 
D)  $1.9037$ 
E)  $10.5562$

Question 18

Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function. 
 
$f ( x ) = \sqrt { 81 - x ^ { 2 } }$

Accepted Answer

A) f is one-to-one 
B) f is not one-to-one 
C) cannot be determined 
A) f is one-to-one 
B) f is not one-to-one 
C) cannot be determined

Question 19

Identify the horizontal asymptote of $g ( x ) = 4 ^ { x + 2 }$ .

Accepted Answer

A) x -axis 
B)  y=2 
C)   y=-2 
D)  y=16 
E)  y=-16 
A) x -axis 
B)  y=2 
C)   y=-2 
D)  y=16 
E)  y=-16

Question 20

Use the properties of logarithms to expand $\ln \sqrt [ 5 ] { \frac { x ^ { 2 } } { x + 3 } }$ .

Accepted Answer

A)  $( \ln x ) ^ { 2 / 5 } - \ln x \cdot \ln 3$ 
B)  $- 5 ( 2 \ln x - \ln ( x + 3 ) )$ 
C)  $\frac { 1 } { 5 } ( 2 \ln x - \ln x \cdot \ln 3 )$ 
D)  $\frac { 2 } { 5 } \ln x - \frac { 1 } { 5 } \ln ( x + 3 )$ 
E)  $\left( \frac { ( \ln x ) ^ { 2 } } { \ln x + \ln 3 } \right) ^ { 1 / 5 }$ 
A)  $( \ln x ) ^ { 2 / 5 } - \ln x \cdot \ln 3$ 
B)  $- 5 ( 2 \ln x - \ln ( x + 3 ) )$ 
C)  $\frac { 1 } { 5 } ( 2 \ln x - \ln x \cdot \ln 3 )$ 
D)  $\frac { 2 } { 5 } \ln x - \frac { 1 } { 5 } \ln ( x + 3 )$ 
E)  $\left( \frac { ( \ln x ) ^ { 2 } } { \ln x + \ln 3 } \right) ^ { 1 / 5 }$

Use the properties of logarithms to condense $4 \ln 3 - 3 \ln x - \ln y$ .

Solve the equation. Do not use a calculator. $4 ^ { x + 6 } = \frac { 1 } { 16 }$

Solve the logarithmic equation. Round your answer to two decimal places. $3 \log _ { 6 } x = 27$

Evaluate the expression $6 ^ { \sqrt { 2 } }$ . Round your answer to three decimal places.

Simplify the expression $\log _ { 6 } 6 ^ { x ^ { 8 } }$ .

Match $f ( x ) = - 3 ^ { x }$ with its graph.

Determine the balance A ( to the nearest cent)for P=500 dollars invested at a rate r=7% for t=10 , compounded 12 times per year. Round the answer to two decimal places.

Determine the balance A ( to the nearest cent)for P=3,000 dollars invested at a rate r=10% for t=10 , compounded one time per year. Round the answer to two decimal places.

Identify the vertical asymptote of $g ( x ) = \log _ { 10 } ( x - 1 )$ .

Evaluate the function as indicated. Round to three decimal places if necessary. 10,000(1.09 t=5.5

An investment is made in an account that pays 9.25%, compounded daily. What is the effective yield for this investment? Round your answer to two decimal places.

Solve the equation. Do not use a calculator. $\log _ { 6 } ( 2 x + 9 ) = \log _ { 6 } ( 4 x + 5 )$

Use the properties of logarithms to condense $6 \log _ { 10 } x - 4 \log _ { 10 } 2$ .

Find $( g \circ f ) ( x )$ where $f ( x ) = 4 x + 7$ and $g ( x ) = x ^ { 2 } - 1$ .

Graph the function $\ln ( x ) = 2 \ln ( x + 3 )$ .

Use $\ln 4 \approx 1.3863$ , $\ln 14 \approx 2.6391$ , and the properties of logarithms to approximate $\ln 56$ to four decimal places.

Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function. $Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function. f ( x ) = \sqrt { 81 - x ^ { 2 } }$ $f ( x ) = \sqrt { 81 - x ^ { 2 } }$

Identify the horizontal asymptote of $g ( x ) = 4 ^ { x + 2 }$ .

Use the properties of logarithms to expand $\ln \sqrt [ 5 ] { \frac { x ^ { 2 } } { x + 3 } }$ .

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

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Exam 9: Exponential and Logarithmic Functions

Use the properties of logarithms to condense 4ln⁡3−3ln⁡x−ln⁡y4 \ln 3 - 3 \ln x - \ln y4ln3−3lnx−lny .

Solve the equation. Do not use a calculator. 4x+6=1164 ^ { x + 6 } = \frac { 1 } { 16 }4x+6=161​

Solve the logarithmic equation. Round your answer to two decimal places. 3log⁡6x=273 \log _ { 6 } x = 273log6​x=27

Evaluate the expression 626 ^ { \sqrt { 2 } }62​ . Round your answer to three decimal places.

Simplify the expression log⁡66x8\log _ { 6 } 6 ^ { x ^ { 8 } }log6​6x8 .

Match f(x)=−3xf ( x ) = - 3 ^ { x }f(x)=−3x with its graph.

Determine the balance A ( to the nearest cent)for P=500 dollars invested at a rate r=7% for t=10 , compounded 12 times per year. Round the answer to two decimal places.

Determine the balance A ( to the nearest cent)for P=3,000 dollars invested at a rate r=10% for t=10 , compounded one time per year. Round the answer to two decimal places.

Identify the vertical asymptote of g(x)=log⁡10(x−1)g ( x ) = \log _ { 10 } ( x - 1 )g(x)=log10​(x−1) .

Evaluate the function as indicated. Round to three decimal places if necessary. 10,000(1.09 t=5.5

An investment is made in an account that pays 9.25%, compounded daily. What is the effective yield for this investment? Round your answer to two decimal places.

Solve the equation. Do not use a calculator. log⁡6(2x+9)=log⁡6(4x+5)\log _ { 6 } ( 2 x + 9 ) = \log _ { 6 } ( 4 x + 5 )log6​(2x+9)=log6​(4x+5)

Use the properties of logarithms to condense 6log⁡10x−4log⁡1026 \log _ { 10 } x - 4 \log _ { 10 } 26log10​x−4log10​2 .

Find (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) where f(x)=4x+7f ( x ) = 4 x + 7f(x)=4x+7 and g(x)=x2−1g ( x ) = x ^ { 2 } - 1g(x)=x2−1 .

Graph the function ln⁡(x)=2ln⁡(x+3)\ln ( x ) = 2 \ln ( x + 3 )ln(x)=2ln(x+3) .

Use ln⁡4≈1.3863\ln 4 \approx 1.3863ln4≈1.3863 , ln⁡14≈2.6391\ln 14 \approx 2.6391ln14≈2.6391 , and the properties of logarithms to approximate ln⁡56\ln 56ln56 to four decimal places.

Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function. f(x)=81−x2f ( x ) = \sqrt { 81 - x ^ { 2 } }f(x)=81−x2​

Identify the horizontal asymptote of g(x)=4x+2g ( x ) = 4 ^ { x + 2 }g(x)=4x+2 .

Use the properties of logarithms to expand ln⁡x2x+35\ln \sqrt [ 5 ] { \frac { x ^ { 2 } } { x + 3 } }ln5x+3x2​​ .

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

Use the properties of logarithms to condense $4 \ln 3 - 3 \ln x - \ln y$ .

Solve the equation. Do not use a calculator. $4 ^ { x + 6 } = \frac { 1 } { 16 }$

Solve the logarithmic equation. Round your answer to two decimal places. $3 \log _ { 6 } x = 27$

Evaluate the expression $6 ^ { \sqrt { 2 } }$ . Round your answer to three decimal places.

Simplify the expression $\log _ { 6 } 6 ^ { x ^ { 8 } }$ .

Match $f ( x ) = - 3 ^ { x }$ with its graph.

Identify the vertical asymptote of $g ( x ) = \log _ { 10 } ( x - 1 )$ .

Solve the equation. Do not use a calculator. $\log _ { 6 } ( 2 x + 9 ) = \log _ { 6 } ( 4 x + 5 )$

Use the properties of logarithms to condense $6 \log _ { 10 } x - 4 \log _ { 10 } 2$ .

Find $( g \circ f ) ( x )$ where $f ( x ) = 4 x + 7$ and $g ( x ) = x ^ { 2 } - 1$ .

Graph the function $\ln ( x ) = 2 \ln ( x + 3 )$ .

Use $\ln 4 \approx 1.3863$ , $\ln 14 \approx 2.6391$ , and the properties of logarithms to approximate $\ln 56$ to four decimal places.

Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function. $Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function. f ( x ) = \sqrt { 81 - x ^ { 2 } }$ $f ( x ) = \sqrt { 81 - x ^ { 2 } }$

Identify the horizontal asymptote of $g ( x ) = 4 ^ { x + 2 }$ .

Use the properties of logarithms to expand $\ln \sqrt [ 5 ] { \frac { x ^ { 2 } } { x + 3 } }$ .