Question 1

For the given functions f and g, find the requested function.
-$f ( x ) = 2 x + 1 ; g ( x ) = 3 x + 9 \quad$ Find $( f \cdot g ) ( x )$

Accepted Answer

A)  $( f \cdot g ) ( x ) = 6 x ^ { 2 } + 9$ 
B)  $( f \cdot g ) ( x ) = 5 x ^ { 2 } + 21 x + 10$ 
C)  $( f \cdot g ) ( x ) = 6 x ^ { 2 } + 12 x + 9$ 
D)  $( f \cdot g ) ( x ) = 6 x ^ { 2 } + 21 x + 9$ 
A)  $( f \cdot g ) ( x ) = 6 x ^ { 2 } + 9$ 
B)  $( f \cdot g ) ( x ) = 5 x ^ { 2 } + 21 x + 10$ 
C)  $( f \cdot g ) ( x ) = 6 x ^ { 2 } + 12 x + 9$ 
D)  $( f \cdot g ) ( x ) = 6 x ^ { 2 } + 21 x + 9$

Question 2

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$\left( \log _ { a } x - \log _ { a } y \right) + 3 \log _ { a } z$

Accepted Answer

A)  $\log _ { a } \frac { x } { z ^ { 3 } y }$ 
B)  $\log _ { a } x z ^ { 3 } y$ 
C)  $\log _ { a } \frac { 3 x z } { y }$ 
D)  $\log _ { a } \frac { x z ^ { 3 } } { y }$ 
A)  $\log _ { a } \frac { x } { z ^ { 3 } y }$ 
B)  $\log _ { a } x z ^ { 3 } y$ 
C)  $\log _ { a } \frac { 3 x z } { y }$ 
D)  $\log _ { a } \frac { x z ^ { 3 } } { y }$

Question 3

Find the value of the logarithmic expression.
-$\log _ { 10 } 10$

Accepted Answer

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

Question 4

Use the following approximations to find the approximate value of the logarithmic expression: 
$\log _ { b } 3 \approx 0.5 \quad \log _ { b } 8 \approx 0.9$
$\log _ { b } 5 \approx 0.7 \quad \log _ { b } 20 \approx 1.3$
-$\log _ { b } \frac { 3 } { 5 }$

Accepted Answer

A)  $0.6$ 
B)  $- 2$ 
C)  $- 0.2$ 
D)  $0.2$ 
A)  $0.6$ 
B)  $- 2$ 
C)  $- 0.2$ 
D)  $0.2$

Question 5

For the given functions f and g, find the composition.
-$f ( x ) = \sqrt { x + 2 } ; g ( x ) = 8 x - 6 \quad$ Find $( g \circ f ) ( x )$

Accepted Answer

A)  $2 \sqrt { 2 x + 1 }$ 
B)  $2 \sqrt { 2 x - 1 }$ 
C)  $8 \sqrt { x - 4 }$ 
D)  $8 \sqrt { x + 2 } - 6$ 
A)  $2 \sqrt { 2 x + 1 }$ 
B)  $2 \sqrt { 2 x - 1 }$ 
C)  $8 \sqrt { x - 4 }$ 
D)  $8 \sqrt { x + 2 } - 6$

Question 6

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. $$\begin{array} { l l l l } 
\text { inverse } & \text { common } & \text { composition symmetric } & \text { exponential } \
\text { vertical } & \text { logarithmic } & \text { natural } \quad \text { half-life } & \text { horizontal }
\end{array}$$
-For a one-to-one function, we can find its ---------function by switching the coordinates of the ordered pairs of the function.

Accepted Answer

A)  symmetric 
B)  natural 
C)  inverse 
D)  composition 
A)  symmetric 
B)  natural 
C)  inverse 
D)  composition

Question 7

Provide an appropriate response.
-Solve $2^{2 x + 1 }= 7$ for $x$. Give an exact solution and a four-decimal-place approximation.

Accepted Answer

A)  $\frac { \log 6 } { 2 \log 2 } ; 1.2925$ 
B)  $\frac { 5 } { 4 } ; 1.2500$ 
C)  $\frac { 1 } { 2 } \left( \frac { \log 2 } { \log 7 } - 1 \right) ; - 0.3219$ 
D)  $\frac { 1 } { 2 } \left( \frac { \log 7 } { \log 2 } - 1 \right) ; 0.9037$ 
A)  $\frac { \log 6 } { 2 \log 2 } ; 1.2925$ 
B)  $\frac { 5 } { 4 } ; 1.2500$ 
C)  $\frac { 1 } { 2 } \left( \frac { \log 2 } { \log 7 } - 1 \right) ; - 0.3219$ 
D)  $\frac { 1 } { 2 } \left( \frac { \log 7 } { \log 2 } - 1 \right) ; 0.9037$

Question 8

Solve the equation.
-$2 ^ { 5 x } = 4$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 1 } { 5 }$ 
C)  $\frac { 5 } { 2 }$ 
D)  $\frac { 2 } { 5 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 1 } { 5 }$ 
C)  $\frac { 5 } { 2 }$ 
D)  $\frac { 2 } { 5 }$

Question 9

Approximate the logarithm to four decimal places using the change of base formula.
-$\log _ { 4 } 2$

Accepted Answer

A)  $2.0000$ 
B)  $- 0.3010$ 
C)  $0.9031$ 
D)  $0.5000$ 
A)  $2.0000$ 
B)  $- 0.3010$ 
C)  $0.9031$ 
D)  $0.5000$

Question 10

Solve the equation.
-$\log _ { 4 } \left( x ^ { 2 } - 3 x \right) = 1$

Accepted Answer

A)  1 
B)  $4 , - 1$ 
C)  4 
D)  $- 4,1$ 
A)  1 
B)  $4 , - 1$ 
C)  4 
D)  $- 4,1$

Question 11

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$\log _ { 10 } 25 + \log _ { 10 } 3 - \log _ { 10 } 15$

Accepted Answer

A)  $\log _ { 10 } 13$ 
B)  $\log _ { 10 } 5$ 
C)  $\log _ { 10 } \frac { 1 } { 5 }$ 
D)  $\log _ { 10 } \frac { 75 } { 15 }$ 
A)  $\log _ { 10 } 13$ 
B)  $\log _ { 10 } 5$ 
C)  $\log _ { 10 } \frac { 1 } { 5 }$ 
D)  $\log _ { 10 } \frac { 75 } { 15 }$

Question 12

Use the power property to rewrite the expression.
-$\log _ { 2 } 3 ^ { - 4 }$

Accepted Answer

A)  $- 4 \log _ { 2 } 3$ 
B)  $- 8 \log 3$ 
C)  $2 \log _ { 4 } 3$ 
D)  $3 \log _ { 2 } 4$ 
A)  $- 4 \log _ { 2 } 3$ 
B)  $- 8 \log 3$ 
C)  $2 \log _ { 4 } 3$ 
D)  $3 \log _ { 2 } 4$

Question 13

Find the exact value.
-$\log 100$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  20 
C)  2 
D)  $\frac { 1 } { 5 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  20 
C)  2 
D)  $\frac { 1 } { 5 }$

Question 14

Determine whether the functions f and g are inverses of each other.
-$f ( x ) = ( x + 7 ) ^ { 3 } + 4 ; g ( x ) = \sqrt [ 3 ] { x - 4 } - 7$

Accepted Answer

A) True 
 B)False

Question 15

Solve the equation.
-$\ln 11 + \ln x = 0$

Accepted Answer

A)  $\frac { 1 } { 11 }$ 
B)  $\sqrt { 11 }$ 
C)  11 
D)  $\varnothing$ 
A)  $\frac { 1 } { 11 }$ 
B)  $\sqrt { 11 }$ 
C)  11 
D)  $\varnothing$

Question 16

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$\log _ { 3 } 8 + \log _ { 3 } x$

Accepted Answer

A)  $\log _ { 3 } ( x + 8 )$ 
B)  $\log _ { 3 } 8 ^ { x }$ 
C)  $\log _ { 24 } x$ 
D)  $\log _ { 3 } 8 x$ 
A)  $\log _ { 3 } ( x + 8 )$ 
B)  $\log _ { 3 } 8 ^ { x }$ 
C)  $\log _ { 24 } x$ 
D)  $\log _ { 3 } 8 x$

Question 17

Use the power property to rewrite the expression.
-$\log _ { 5 } \sqrt [ 7 ] { \mathrm { y } }$

Accepted Answer

A)  $7 \log _ { 5 } y$ 
B)  $\frac { 1 } { 7 } \log _ { 5 } \sqrt [ 7 ] { \mathrm { y } }$ 
C)  $\frac { 1 } { 7 } \log _ { 5 } y$ 
D)  $\frac { 1 } { 5 } \log _ { 7 } y$ 
A)  $7 \log _ { 5 } y$ 
B)  $\frac { 1 } { 7 } \log _ { 5 } \sqrt [ 7 ] { \mathrm { y } }$ 
C)  $\frac { 1 } { 7 } \log _ { 5 } y$ 
D)  $\frac { 1 } { 5 } \log _ { 7 } y$

Question 18

Determine whether the given graph is the graph of a one-to-one function.
-

Accepted Answer

A)  one-to-one 
B)  not one-to-one 
A)  one-to-one 
B)  not one-to-one

Question 19

Find the exact value.
-$\ln \sqrt [ 3 ] { \mathrm { e } }$

Accepted Answer

A)  $\frac { 1 } { 3 }$ 
B)  $\frac { e } { 3 }$ 
C)  $3 \mathrm { e }$ 
D)  3 
A)  $\frac { 1 } { 3 }$ 
B)  $\frac { e } { 3 }$ 
C)  $3 \mathrm { e }$ 
D)  3

Question 20

Solve the equation for x. Give an approximate solution accurate to four decimal places.
-$\ln ( 13 x + 6 ) = - 1.1$

Accepted Answer

A)  $- 0.9445$ 
B)  $- 0.4359$ 
C)  $- 5.6671$ 
D)  $- 73.6723$ 
A)  $- 0.9445$ 
B)  $- 0.4359$ 
C)  $- 5.6671$ 
D)  $- 73.6723$

For the given functions f and g, find the requested function. - $f ( x ) = 2 x + 1 ; g ( x ) = 3 x + 9 \quad$ Find $( f \cdot g ) ( x )$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\left( \log _ { a } x - \log _ { a } y \right) + 3 \log _ { a } z$

Find the value of the logarithmic expression. - $\log _ { 10 } 10$

Use the following approximations to find the approximate value of the logarithmic expression: $\log _ { b } 3 \approx 0.5 \quad \log _ { b } 8 \approx 0.9$ $\log _ { b } 5 \approx 0.7 \quad \log _ { b } 20 \approx 1.3$ - $\log _ { b } \frac { 3 } { 5 }$

For the given functions f and g, find the composition. - $f ( x ) = \sqrt { x + 2 } ; g ( x ) = 8 x - 6 \quad$ Find $( g \circ f ) ( x )$

Provide an appropriate response. -Solve $2^{2 x + 1 }= 7$ for $x$ . Give an exact solution and a four-decimal-place approximation.

Solve the equation. - $2 ^ { 5 x } = 4$

Approximate the logarithm to four decimal places using the change of base formula. - $\log _ { 4 } 2$

Solve the equation. - $\log _ { 4 } \left( x ^ { 2 } - 3 x \right) = 1$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 10 } 25 + \log _ { 10 } 3 - \log _ { 10 } 15$

Use the power property to rewrite the expression. - $\log _ { 2 } 3 ^ { - 4 }$

Find the exact value. - $\log 100$

Determine whether the functions f and g are inverses of each other. - $f ( x ) = ( x + 7 ) ^ { 3 } + 4 ; g ( x ) = \sqrt [ 3 ] { x - 4 } - 7$

Solve the equation. - $\ln 11 + \ln x = 0$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 3 } 8 + \log _ { 3 } x$

Use the power property to rewrite the expression. - $\log _ { 5 } \sqrt [ 7 ] { \mathrm { y } }$

Determine whether the given graph is the graph of a one-to-one function. -

Find the exact value. - $\ln \sqrt [ 3 ] { \mathrm { e } }$

Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\ln ( 13 x + 6 ) = - 1.1$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 12: Exponential and Logarithmic Functions

For the given functions f and g, find the requested function. - f(x)=2x+1;g(x)=3x+9f ( x ) = 2 x + 1 ; g ( x ) = 3 x + 9 \quadf(x)=2x+1;g(x)=3x+9 Find (f⋅g)(x)( f \cdot g ) ( x )(f⋅g)(x)

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - (log⁡ax−log⁡ay)+3log⁡az\left( \log _ { a } x - \log _ { a } y \right) + 3 \log _ { a } z(loga​x−loga​y)+3loga​z

Find the value of the logarithmic expression. - log⁡1010\log _ { 10 } 10log10​10

For the given functions f and g, find the composition. - f(x)=x+2;g(x)=8x−6f ( x ) = \sqrt { x + 2 } ; g ( x ) = 8 x - 6 \quadf(x)=x+2​;g(x)=8x−6 Find (g∘f)(x)( g \circ f ) ( x )(g∘f)(x)

Provide an appropriate response. -Solve 22x+1=72^{2 x + 1 }= 722x+1=7 for xxx . Give an exact solution and a four-decimal-place approximation.

Solve the equation. - 25x=42 ^ { 5 x } = 425x=4

Approximate the logarithm to four decimal places using the change of base formula. - log⁡42\log _ { 4 } 2log4​2

Solve the equation. - log⁡4(x2−3x)=1\log _ { 4 } \left( x ^ { 2 } - 3 x \right) = 1log4​(x2−3x)=1

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - log⁡1025+log⁡103−log⁡1015\log _ { 10 } 25 + \log _ { 10 } 3 - \log _ { 10 } 15log10​25+log10​3−log10​15

Use the power property to rewrite the expression. - log⁡23−4\log _ { 2 } 3 ^ { - 4 }log2​3−4

Find the exact value. - log⁡100\log 100log100

Determine whether the functions f and g are inverses of each other. - f(x)=(x+7)3+4;g(x)=x−43−7f ( x ) = ( x + 7 ) ^ { 3 } + 4 ; g ( x ) = \sqrt [ 3 ] { x - 4 } - 7f(x)=(x+7)3+4;g(x)=3x−4​−7

Solve the equation. - ln⁡11+ln⁡x=0\ln 11 + \ln x = 0ln11+lnx=0

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - log⁡38+log⁡3x\log _ { 3 } 8 + \log _ { 3 } xlog3​8+log3​x

Use the power property to rewrite the expression. - log⁡5y7\log _ { 5 } \sqrt [ 7 ] { \mathrm { y } }log5​7y​