Question 1

$\frac { \log _ { 9 } 486 } { \log _ { 9 } 54 } = 1$

Accepted Answer

A) True 
 B)False

Question 2

For the given functions f and g, find the requested function.
-$f ( x ) = \sqrt { x } ; g ( x ) = 4 x - 9 \quad$ Find $\left( \frac { f } { g } \right) ( x )$

Accepted Answer

A)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 4 \mathrm { x } - 4 }$, where $x \neq 1$ 
B)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 4 \mathrm { x } - 9 }$, where $x \neq \frac { 9 } { 4 }$ 
C)  $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 9 - 4 x }$, where $x \neq \frac { 9 } { 4 }$ 
D)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 9 - 4 \mathrm { x } } { \sqrt { \mathrm { x } } }$, where $x \neq 0$ 
A)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 4 \mathrm { x } - 4 }$, where $x \neq 1$ 
B)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 4 \mathrm { x } - 9 }$, where $x \neq \frac { 9 } { 4 }$ 
C)  $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 9 - 4 x }$, where $x \neq \frac { 9 } { 4 }$ 
D)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 9 - 4 \mathrm { x } } { \sqrt { \mathrm { x } } }$, where $x \neq 0$

Question 3

Solve.
-A city has been growing at a rate of $0.8 \%$ annually. If there are currently $3,392,000$ residents in the city, how many (to the nearest ten-thousand) would be living in this city six years from now? Use $y = 3,392,000 ( 2.7 ) ^ { 0.008 t }$.

Accepted Answer

A)  $9,160,000$ 
B)  440,000 
C)  $3,590,000$ 
D)  $3,560,000$ 
A)  $9,160,000$ 
B)  440,000 
C)  $3,590,000$ 
D)  $3,560,000$

Question 4

Solve the equation.
-$27^{ ( 3 x - 2 ) }= 9 ^ { 5 x }$

Accepted Answer

A)  6 
B)  $- \frac { 1 } { 6 }$ 
C)  $- 6$ 
D)  $\frac { 1 } { 6 }$ 
A)  6 
B)  $- \frac { 1 } { 6 }$ 
C)  $- 6$ 
D)  $\frac { 1 } { 6 }$

Question 5

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$\log _ { 7 } ( x - 6 ) - \log _ { 7 } ( x + 2 )$

Accepted Answer

A)  $\log _ { 7 } \frac { x - 6 } { x + 2 }$ 
B)  $\log _ { 7 } - 8$ 
C)  $\log _ { 7 } \frac { x - 6 } { x - 2 }$ 
D)  $\log _ { 7 } \left( x ^ { 2 } - 4 x - 12 \right)$ 
A)  $\log _ { 7 } \frac { x - 6 } { x + 2 }$ 
B)  $\log _ { 7 } - 8$ 
C)  $\log _ { 7 } \frac { x - 6 } { x - 2 }$ 
D)  $\log _ { 7 } \left( x ^ { 2 } - 4 x - 12 \right)$

Question 6

Determine whether the functions f and g are inverses of each other.
-$f ( x ) = x ^ { 3 } + 6 ; g ( x ) = \sqrt [ 3 ] { x } - 6$

Accepted Answer

A) True 
 B)False

Question 7

Solve the logarithmic equation for x. Give an exact solution
-$\log _ { 5 } 3 + \log _ { 5 } x = 1$

Accepted Answer

A)  $\frac { 5 } { 3 }$ 
B)  $\frac { 3 } { 5 }$ 
C)  $\frac { 1 } { 3 }$ 
A)  $\frac { 5 } { 3 }$ 
B)  $\frac { 3 } { 5 }$ 
C)  $\frac { 1 } { 3 }$

Question 8

Solve the equation.
-$2 ^{( 7 + 3 x )} = \frac { 1 } { 4 }$

Accepted Answer

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

Question 9

Write as an exponential equation.
-$\log _ { 1 / 4 } 256 = - 4$

Accepted Answer

A)  $256 ^ { 1 / 4 } = 4$ 
B)  $\left( \frac { 1 } { 4 } \right) ^ { - 4 } = 256$ 
C)  $( - 4 ) ^ { 1 / 4 } = 256$ 
D)  $\left( \frac { 1 } { 4 } \right) ^ { 4 } = 256$ 
A)  $256 ^ { 1 / 4 } = 4$ 
B)  $\left( \frac { 1 } { 4 } \right) ^ { - 4 } = 256$ 
C)  $( - 4 ) ^ { 1 / 4 } = 256$ 
D)  $\left( \frac { 1 } { 4 } \right) ^ { 4 } = 256$

Question 10

Use a calculator to approximate the logarithm to four decimal places.
-$\log 0.00390$

Accepted Answer

A)  $- 2.4202$ 
B)  $- 2.3979$ 
C)  $- 2.4089$ 
D)  $- 5.5468$ 
A)  $- 2.4202$ 
B)  $- 2.3979$ 
C)  $- 2.4089$ 
D)  $- 5.5468$

Question 11

Graph the exponential function.
-$f(x)=4^{x}$

Accepted Answer

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

Question 12

The reliability of a new model of CD player can be described by the exponential function R(t) = 2.7-S1U1P1(1/3S1S1P0)S1U1P1tS1S1P0, where the
reliability R is the probability (as a decimal) that the CD player is still working t years after it is manufactured. Round the
answer to the nearest hundredth. Then write your answer as a percent.
-What is the probability that the CD player will still work $\frac { 1 } { 4 }$ of a year after it is manufactured?

Accepted Answer

A)  $9 \%$ 
B)  $92 \%$ 
C)  $72 \%$ 
D)  $27 \%$ 
A)  $9 \%$ 
B)  $92 \%$ 
C)  $72 \%$ 
D)  $27 \%$

Question 13

Solve the equation. Give an approximate solution to four decimal places.
-$e ^ { ( x + 3 ) } = 5$

Accepted Answer

A)  $2.0794$ 
B)  $- 1.2953$ 
C)  $- 0.9206$ 
D)  $- 1.3906$ 
A)  $2.0794$ 
B)  $- 1.2953$ 
C)  $- 0.9206$ 
D)  $- 1.3906$

Question 14

The graph of an exponential function is given. Match the graph to one of the following functions.
-

Accepted Answer

A)  $f ( x ) = 2 ^ { x }$ 
B)  $f ( x ) = 2 ^ { x + 2 }$ 
C)  $f ( x ) = 2 ^ { x } - 2$ 
D)  $f ( x ) = 2 ^ { x } + 2$ 
A)  $f ( x ) = 2 ^ { x }$ 
B)  $f ( x ) = 2 ^ { x + 2 }$ 
C)  $f ( x ) = 2 ^ { x } - 2$ 
D)  $f ( x ) = 2 ^ { x } + 2$

Question 15

For the given functions f and g, find the composition.
-$f ( x ) = 6 x ^ { 2 } + 4 x ; g ( x ) = 3 x \quad$ Find $( f \circ g ) ( x )$.

Accepted Answer

A)  $18 x ^ { 3 } + 12 x ^ { 2 }$ 
B)  $54 x ^ { 2 } + 12 x$ 
C)  $6 x ^ { 2 } + 7$ 
D)  $18 x ^ { 2 } + 12 x$ 
A)  $18 x ^ { 3 } + 12 x ^ { 2 }$ 
B)  $54 x ^ { 2 } + 12 x$ 
C)  $6 x ^ { 2 } + 7$ 
D)  $18 x ^ { 2 } + 12 x$

Question 16

Determine whether the function is a one-to-one function.
-

Accepted Answer

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

Question 17

Graph the exponential function.
-$f(x)=4^{x+1}$

Accepted Answer

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

Question 18

Graph the inverse of the function on the same set of axes.
-

Accepted Answer

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

Question 19

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. $$\begin{array} { l l l l } 
\text { inverse } & \text { common } & \text { composition symmetric } & \text { exponential } \
\text { vertical } & \text { logarithmic } & \text { natural } \quad \text { half-life } & \text { horizontal }
\end{array}$$
-To see whether a graph is the graph of a one-to-one function, apply the--------- line test to see whether it is a function, and then apply the ----------line test to see whether it is a one-to-one
Function.

Accepted Answer

A)  vertical; horizontal 
B)  vertical; exponential 
C)  horizontal; inverse 
D)  horizontal; vertical 
A)  vertical; horizontal 
B)  vertical; exponential 
C)  horizontal; inverse 
D)  horizontal; vertical

Question 20

Find the exact value.
-$\log \left( \frac { 1 } { 100 } \right)$

Accepted Answer

A)  $- 2$ 
B)  $\frac { 1 } { 100 }$ 
C)  $- \frac { 1 } { 2 }$ 
D)  2 
A)  $- 2$ 
B)  $\frac { 1 } { 100 }$ 
C)  $- \frac { 1 } { 2 }$ 
D)  2

$\frac { \log _ { 9 } 486 } { \log _ { 9 } 54 } = 1$

For the given functions f and g, find the requested function. - $f ( x ) = \sqrt { x } ; g ( x ) = 4 x - 9 \quad$ Find $\left( \frac { f } { g } \right) ( x )$

Solve. -A city has been growing at a rate of $0.8 \%$ annually. If there are currently $3,392,000$ residents in the city, how many (to the nearest ten-thousand) would be living in this city six years from now? Use $y = 3,392,000 ( 2.7 ) ^ { 0.008 t }$ .

Solve the equation. - $27^{ ( 3 x - 2 ) }= 9 ^ { 5 x }$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 7 } ( x - 6 ) - \log _ { 7 } ( x + 2 )$

Determine whether the functions f and g are inverses of each other. - $f ( x ) = x ^ { 3 } + 6 ; g ( x ) = \sqrt [ 3 ] { x } - 6$

Solve the logarithmic equation for x. Give an exact solution - $\log _ { 5 } 3 + \log _ { 5 } x = 1$

Solve the equation. - $2 ^{( 7 + 3 x )} = \frac { 1 } { 4 }$

Write as an exponential equation. - $\log _ { 1 / 4 } 256 = - 4$

Use a calculator to approximate the logarithm to four decimal places. - $\log 0.00390$

Graph the exponential function. - $f(x)=4^{x}$ $Graph the exponential function. - f(x)=4^{x}$

Solve the equation. Give an approximate solution to four decimal places. - $e ^ { ( x + 3 ) } = 5$

The graph of an exponential function is given. Match the graph to one of the following functions. -

For the given functions f and g, find the composition. - $f ( x ) = 6 x ^ { 2 } + 4 x ; g ( x ) = 3 x \quad$ Find $( f \circ g ) ( x )$ .

Determine whether the function is a one-to-one function. -

Graph the exponential function. - $f(x)=4^{x+1}$ $Graph the exponential function. - f(x)=4^{x+1}$

Graph the inverse of the function on the same set of axes. -

Find the exact value. - $\log \left( \frac { 1 } { 100 } \right)$

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

log⁡9486log⁡954=1\frac { \log _ { 9 } 486 } { \log _ { 9 } 54 } = 1log9​54log9​486​=1

For the given functions f and g, find the requested function. - f(x)=x;g(x)=4x−9f ( x ) = \sqrt { x } ; g ( x ) = 4 x - 9 \quadf(x)=x​;g(x)=4x−9 Find (fg)(x)\left( \frac { f } { g } \right) ( x )(gf​)(x)

Solve the equation. - 27(3x−2)=95x27^{ ( 3 x - 2 ) }= 9 ^ { 5 x }27(3x−2)=95x

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - log⁡7(x−6)−log⁡7(x+2)\log _ { 7 } ( x - 6 ) - \log _ { 7 } ( x + 2 )log7​(x−6)−log7​(x+2)

Determine whether the functions f and g are inverses of each other. - f(x)=x3+6;g(x)=x3−6f ( x ) = x ^ { 3 } + 6 ; g ( x ) = \sqrt [ 3 ] { x } - 6f(x)=x3+6;g(x)=3x​−6

Solve the logarithmic equation for x. Give an exact solution - log⁡53+log⁡5x=1\log _ { 5 } 3 + \log _ { 5 } x = 1log5​3+log5​x=1

Solve the equation. - 2(7+3x)=142 ^{( 7 + 3 x )} = \frac { 1 } { 4 }2(7+3x)=41​

Write as an exponential equation. - log⁡1/4256=−4\log _ { 1 / 4 } 256 = - 4log1/4​256=−4

Use a calculator to approximate the logarithm to four decimal places. - log⁡0.00390\log 0.00390log0.00390

Graph the exponential function. - f(x)=4xf(x)=4^{x}f(x)=4x

Solve the equation. Give an approximate solution to four decimal places. - e(x+3)=5e ^ { ( x + 3 ) } = 5e(x+3)=5

The graph of an exponential function is given. Match the graph to one of the following functions. -

For the given functions f and g, find the composition. - f(x)=6x2+4x;g(x)=3xf ( x ) = 6 x ^ { 2 } + 4 x ; g ( x ) = 3 x \quadf(x)=6x2+4x;g(x)=3x Find (f∘g)(x)( f \circ g ) ( x )(f∘g)(x) .

Determine whether the function is a one-to-one function. -

Graph the exponential function. - f(x)=4x+1f(x)=4^{x+1}f(x)=4x+1

Graph the inverse of the function on the same set of axes. -

Find the exact value. - log⁡(1100)\log \left( \frac { 1 } { 100 } \right)log(1001​)

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

$\frac { \log _ { 9 } 486 } { \log _ { 9 } 54 } = 1$

For the given functions f and g, find the requested function. - $f ( x ) = \sqrt { x } ; g ( x ) = 4 x - 9 \quad$ Find $\left( \frac { f } { g } \right) ( x )$

Solve the equation. - $27^{ ( 3 x - 2 ) }= 9 ^ { 5 x }$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 7 } ( x - 6 ) - \log _ { 7 } ( x + 2 )$

Determine whether the functions f and g are inverses of each other. - $f ( x ) = x ^ { 3 } + 6 ; g ( x ) = \sqrt [ 3 ] { x } - 6$

Solve the logarithmic equation for x. Give an exact solution - $\log _ { 5 } 3 + \log _ { 5 } x = 1$

Solve the equation. - $2 ^{( 7 + 3 x )} = \frac { 1 } { 4 }$

Write as an exponential equation. - $\log _ { 1 / 4 } 256 = - 4$

Use a calculator to approximate the logarithm to four decimal places. - $\log 0.00390$

Graph the exponential function. - $f(x)=4^{x}$ $Graph the exponential function. - f(x)=4^{x}$

Solve the equation. Give an approximate solution to four decimal places. - $e ^ { ( x + 3 ) } = 5$

For the given functions f and g, find the composition. - $f ( x ) = 6 x ^ { 2 } + 4 x ; g ( x ) = 3 x \quad$ Find $( f \circ g ) ( x )$ .

Graph the exponential function. - $f(x)=4^{x+1}$ $Graph the exponential function. - f(x)=4^{x+1}$

Find the exact value. - $\log \left( \frac { 1 } { 100 } \right)$