Question 1

Use the exponential growth formula to find the final amount. Round to the nearest whole.
-

Accepted Answer

A)  16,032 
B)  13,398 
C)  14,660 
D)  44,573 
A)  16,032 
B)  13,398 
C)  14,660 
D)  44,573

Question 2

Approximate the logarithm to four decimal places using the change of base formula.
-$\log _{1 / 5} 3$

Accepted Answer

A)  $- 0.2218$ 
B)  $- 0.6826$ 
C)  $1.1761$ 
D)  $- 1.4650$ 
A)  $- 0.2218$ 
B)  $- 0.6826$ 
C)  $1.1761$ 
D)  $- 1.4650$

Question 3

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$6 \log _ { b } x - \log _ { b } y$

Accepted Answer

A)  $\log _ { b } x ^ { 6 } \div \log _ { b } y$ 
B)  $\log _ { b } \frac { x ^ { 6 } } { y }$ 
C)  $\log _ { b } \left( x ^ { 6 } - y \right)$ 
D)  $\log _ { b } \frac { 6 x } { y }$ 
A)  $\log _ { b } x ^ { 6 } \div \log _ { b } y$ 
B)  $\log _ { b } \frac { x ^ { 6 } } { y }$ 
C)  $\log _ { b } \left( x ^ { 6 } - y \right)$ 
D)  $\log _ { b } \frac { 6 x } { y }$

Question 4

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. $$\begin{array} { l l l l } 
\text { inverse } & \text { common } & \text { composition symmetric } & \text { exponential } \
\text { vertical } & \text { logarithmic } & \text { natural } \quad \text { half-life } & \text { horizontal }
\end{array}$$
-A quantity that grows or decays by the same percent at regular time periods is said to have ---------- growth or decay.

Accepted Answer

A)  common 
B)  exponential 
C)  logarithmic 
D)  natural 
A)  common 
B)  exponential 
C)  logarithmic 
D)  natural

Question 5

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

Accepted Answer

A)  $( f + g ) ( x ) = 7 x$ 
B)  $( f + g ) ( x ) = 3 x + 3$ 
C)  $( f + g ) ( x ) = 4 x + 3$ 
D)  $( f + g ) ( x ) = 3 x ^ { 2 } + 7 x + 2$ 
A)  $( f + g ) ( x ) = 7 x$ 
B)  $( f + g ) ( x ) = 3 x + 3$ 
C)  $( f + g ) ( x ) = 4 x + 3$ 
D)  $( f + g ) ( x ) = 3 x ^ { 2 } + 7 x + 2$

Question 6

Solve the equation.
-$\log _ { 3 } ( 5 x + 3 ) = \log _ { 3 } ( 5 x + 7 )$

Accepted Answer

A)  0 
B)  $\frac { 5 } { 2 }$ 
C)  $\varnothing$ 
D)  2 
A)  0 
B)  $\frac { 5 } { 2 }$ 
C)  $\varnothing$ 
D)  2

Question 7

Solve the equation.
-$3125 ^ { x } = \frac { 1 } { 625 }$

Accepted Answer

A)  $- \frac { 4 } { 5 }$ 
B)  $\frac { 5 } { 4 }$ 
C)  $\frac { 4 } { 5 }$ 
D)  $- \frac { 5 } { 4 }$ 
A)  $- \frac { 4 } { 5 }$ 
B)  $\frac { 5 } { 4 }$ 
C)  $\frac { 4 } { 5 }$ 
D)  $- \frac { 5 } { 4 }$

Question 8

For the given functions f and g, find the requested function.
-$f ( x ) = 6 x + 1 ; g ( x ) = 3 x - 5 \quad$ Find $\left( \frac { f } { g } \right) ( x )$

Accepted Answer

A)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 3 \mathrm { x } - 5 } { 6 \mathrm { x } + 1 }$, where $x \neq - \frac { 1 } { 6 }$ 
B)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 3 \mathrm { x } + 5 } { 6 \mathrm { x } + 1 }$, where $x \neq - \frac { 1 } { 6 }$ 
C)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 6 \mathrm { x } + 1 } { 3 \mathrm { x } + 5 }$, where $x \neq - \frac { 5 } { 3 }$ 
D)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 6 \mathrm { x } + 1 } { 3 \mathrm { x } - 5 }$, where $x \neq \frac { 5 } { 3 }$ 
A)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 3 \mathrm { x } - 5 } { 6 \mathrm { x } + 1 }$, where $x \neq - \frac { 1 } { 6 }$ 
B)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 3 \mathrm { x } + 5 } { 6 \mathrm { x } + 1 }$, where $x \neq - \frac { 1 } { 6 }$ 
C)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 6 \mathrm { x } + 1 } { 3 \mathrm { x } + 5 }$, where $x \neq - \frac { 5 } { 3 }$ 
D)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 6 \mathrm { x } + 1 } { 3 \mathrm { x } - 5 }$, where $x \neq \frac { 5 } { 3 }$

Question 9

Use the exponential growth formula to find the final amount. Round to the nearest whole.
-

Accepted Answer

A)  54 
B)  50,821 
C)  38,389 
D)  38,995 
A)  54 
B)  50,821 
C)  38,389 
D)  38,995

Question 10

Solve the equation for x. Give an exact solution.
-$\log x = 2.8$

Accepted Answer

A)  $\mathrm { e } ^ { 2.8 }$ 
B)  $2.8 ^ { 10 }$ 
C)  $10 ^ { 2.8 }$ 
D)  $2.8 ^ { \mathrm { e } }$ 
A)  $\mathrm { e } ^ { 2.8 }$ 
B)  $2.8 ^ { 10 }$ 
C)  $10 ^ { 2.8 }$ 
D)  $2.8 ^ { \mathrm { e } }$

Question 11

For the given functions f and g, find the composition.
-$f ( x ) = \sqrt { x + 5 } ; g ( x ) = 2 x \quad$ Find $( f \circ g ) ( 2 )$.

Accepted Answer

A)  3 
B)  $\sqrt { 14 }$ 
C)  $2 \sqrt { 14 }$ 
D)  $2 \sqrt { 7 }$ 
A)  3 
B)  $\sqrt { 14 }$ 
C)  $2 \sqrt { 14 }$ 
D)  $2 \sqrt { 7 }$

Question 12

Graph the function.
-$y = \log _ { 1 / 2 } x$

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$\log _ { 7 } 6 + \log _ { 7 } 13$

Accepted Answer

A)  $\log _ { 14 } 78$ 
B)  $\log _ { 7 } 78$ 
C)  $\log _ { 14 } 19$ 
D)  $\log _ { 7 } 19$ 
A)  $\log _ { 14 } 78$ 
B)  $\log _ { 7 } 78$ 
C)  $\log _ { 14 } 19$ 
D)  $\log _ { 7 } 19$

Question 15

For the given functions f and g, find the requested function.
-If $f ( x ) = 4 x ^ { 2 } + 6 x + 5$ and $g ( x ) = 6 x - 4$, find $( g f ) ( x )$.

Accepted Answer

A)  $24 x ^ { 2 } + 36 x + 26$ 
B)  $24 x ^ { 2 } + 36 x + 34$ 
C)  $4 x ^ { 2 } + 6 x + 1$ 
D)  $4 x ^ { 2 } + 36 x + 26$ 
A)  $24 x ^ { 2 } + 36 x + 26$ 
B)  $24 x ^ { 2 } + 36 x + 34$ 
C)  $4 x ^ { 2 } + 6 x + 1$ 
D)  $4 x ^ { 2 } + 36 x + 26$

Question 16

Graph the exponential function.
-$f(x)=\left(\frac{1}{5}\right)^{x+1}$

Accepted Answer

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

Question 17

For the given functions f and g, find the requested function.
-$f ( x ) = x ^ { 2 } - 3 \sqrt [ 3 ] { x } ; g ( x ) = x - 5 \quad$ Find $\left( \frac { f } { g } \right) ( x )$

Accepted Answer

A)  $\left( \frac { f } { g } \right) ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 3 x \sqrt [ 3 ] { x } + 15 \sqrt [ 3 ] { x }$ 
B)  $\left( \frac { f } { g } \right) ( x ) = \frac { x ^ { 2 } - 3 \sqrt [ 3 ] { x } } { x - 5 }$, where $x \neq 0$ 
C)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \mathrm { x } ^ { 2 } - 3 \sqrt [ 3 ] { \mathrm { x } } } { \mathrm { x } - 5 }$, where $x \neq 5$ 
D)  $\left( \frac { f } { g } \right) ( x ) = \frac { x ^ { 2 } - 3 \sqrt [ 3 ] { x } } { x - 5 }$, where $x \neq - 5$ 
A)  $\left( \frac { f } { g } \right) ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 3 x \sqrt [ 3 ] { x } + 15 \sqrt [ 3 ] { x }$ 
B)  $\left( \frac { f } { g } \right) ( x ) = \frac { x ^ { 2 } - 3 \sqrt [ 3 ] { x } } { x - 5 }$, where $x \neq 0$ 
C)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \mathrm { x } ^ { 2 } - 3 \sqrt [ 3 ] { \mathrm { x } } } { \mathrm { x } - 5 }$, where $x \neq 5$ 
D)  $\left( \frac { f } { g } \right) ( x ) = \frac { x ^ { 2 } - 3 \sqrt [ 3 ] { x } } { x - 5 }$, where $x \neq - 5$

Question 18

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x).
-$h ( x ) = \left( 9 - 3 x ^ { 3 } \right) ^ { 2 }$

Accepted Answer

A)  $f ( x ) = x ^ { 2 } ; g ( x ) = 9 - 3 x$ 
B)  $f ( x ) = x ^ { 2 } ; g ( x ) = 9 - 3 x ^ { 3 }$ 
C)  $f ( x ) = 9 - 3 x ^ { 2 } ; g ( x ) = x ^ { 3 }$ 
D)  $f ( x ) = 9 - 3 x ^ { 3 } ; g ( x ) = x ^ { 2 }$ 
A)  $f ( x ) = x ^ { 2 } ; g ( x ) = 9 - 3 x$ 
B)  $f ( x ) = x ^ { 2 } ; g ( x ) = 9 - 3 x ^ { 3 }$ 
C)  $f ( x ) = 9 - 3 x ^ { 2 } ; g ( x ) = x ^ { 3 }$ 
D)  $f ( x ) = 9 - 3 x ^ { 3 } ; g ( x ) = x ^ { 2 }$

Question 19

Use a calculator to approximate the logarithm to four decimal places.
-$\log 4.60$

Accepted Answer

A)  $0.6721$ 
B)  $1.5261$ 
C)  $0.6628$ 
D)  $0.6532$ 
A)  $0.6721$ 
B)  $1.5261$ 
C)  $0.6628$ 
D)  $0.6532$

Question 20

Use a calculator to approximate the logarithm to four decimal places.
-$\log 0.0509$

Accepted Answer

A)  $- 1.3019$ 
B)  $- 1.2848$ 
C)  $- 1.2933$ 
D)  $- 2.9779$ 
A)  $- 1.3019$ 
B)  $- 1.2848$ 
C)  $- 1.2933$ 
D)  $- 2.9779$

Use the exponential growth formula to find the final amount. Round to the nearest whole. -

Approximate the logarithm to four decimal places using the change of base formula. - $\log _{1 / 5} 3$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $6 \log _ { b } x - \log _ { b } y$

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

Solve the equation. - $\log _ { 3 } ( 5 x + 3 ) = \log _ { 3 } ( 5 x + 7 )$

Solve the equation. - $3125 ^ { x } = \frac { 1 } { 625 }$

For the given functions f and g, find the requested function. - $f ( x ) = 6 x + 1 ; g ( x ) = 3 x - 5 \quad$ Find $\left( \frac { f } { g } \right) ( x )$

Use the exponential growth formula to find the final amount. Round to the nearest whole. -

Solve the equation for x. Give an exact solution. - $\log x = 2.8$

For the given functions f and g, find the composition. - $f ( x ) = \sqrt { x + 5 } ; g ( x ) = 2 x \quad$ Find $( f \circ g ) ( 2 )$ .

Graph the function. - $y = \log _ { 1 / 2 } x$ $Graph the function. - y = \log _ { 1 / 2 } x$

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

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 7 } 6 + \log _ { 7 } 13$

For the given functions f and g, find the requested function. -If $f ( x ) = 4 x ^ { 2 } + 6 x + 5$ and $g ( x ) = 6 x - 4$ , find $( g f ) ( x )$ .

Graph the exponential function. - $f(x)=\left(\frac{1}{5}\right)^{x+1}$ $Graph the exponential function. - f(x)=\left(\frac{1}{5}\right)^{x+1}$

For the given functions f and g, find the requested function. - $f ( x ) = x ^ { 2 } - 3 \sqrt [ 3 ] { x } ; g ( x ) = x - 5 \quad$ Find $\left( \frac { f } { g } \right) ( x )$

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x). - $h ( x ) = \left( 9 - 3 x ^ { 3 } \right) ^ { 2 }$

Use a calculator to approximate the logarithm to four decimal places. - $\log 4.60$

Use a calculator to approximate the logarithm to four decimal places. - $\log 0.0509$

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

Use the exponential growth formula to find the final amount. Round to the nearest whole. -

Approximate the logarithm to four decimal places using the change of base formula. - log⁡1/53\log _{1 / 5} 3log1/5​3

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - 6log⁡bx−log⁡by6 \log _ { b } x - \log _ { b } y6logb​x−logb​y

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

Solve the equation. - log⁡3(5x+3)=log⁡3(5x+7)\log _ { 3 } ( 5 x + 3 ) = \log _ { 3 } ( 5 x + 7 )log3​(5x+3)=log3​(5x+7)

Solve the equation. - 3125x=16253125 ^ { x } = \frac { 1 } { 625 }3125x=6251​

For the given functions f and g, find the requested function. - f(x)=6x+1;g(x)=3x−5f ( x ) = 6 x + 1 ; g ( x ) = 3 x - 5 \quadf(x)=6x+1;g(x)=3x−5 Find (fg)(x)\left( \frac { f } { g } \right) ( x )(gf​)(x)

Use the exponential growth formula to find the final amount. Round to the nearest whole. -

Solve the equation for x. Give an exact solution. - log⁡x=2.8\log x = 2.8logx=2.8

For the given functions f and g, find the composition. - f(x)=x+5;g(x)=2xf ( x ) = \sqrt { x + 5 } ; g ( x ) = 2 x \quadf(x)=x+5​;g(x)=2x Find (f∘g)(2)( f \circ g ) ( 2 )(f∘g)(2) .

Graph the function. - y=log⁡1/2xy = \log _ { 1 / 2 } xy=log1/2​x

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

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - log⁡76+log⁡713\log _ { 7 } 6 + \log _ { 7 } 13log7​6+log7​13

For the given functions f and g, find the requested function. -If f(x)=4x2+6x+5f ( x ) = 4 x ^ { 2 } + 6 x + 5f(x)=4x2+6x+5 and g(x)=6x−4g ( x ) = 6 x - 4g(x)=6x−4 , find (gf)(x)( g f ) ( x )(gf)(x) .

Graph the exponential function. - f(x)=(15)x+1f(x)=\left(\frac{1}{5}\right)^{x+1}f(x)=(51​)x+1

For the given functions f and g, find the requested function. - f(x)=x2−3x3;g(x)=x−5f ( x ) = x ^ { 2 } - 3 \sqrt [ 3 ] { x } ; g ( x ) = x - 5 \quadf(x)=x2−33x​;g(x)=x−5 Find (fg)(x)\left( \frac { f } { g } \right) ( x )(gf​)(x)

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x). - h(x)=(9−3x3)2h ( x ) = \left( 9 - 3 x ^ { 3 } \right) ^ { 2 }h(x)=(9−3x3)2

Use a calculator to approximate the logarithm to four decimal places. - log⁡4.60\log 4.60log4.60

Use a calculator to approximate the logarithm to four decimal places. - log⁡0.0509\log 0.0509log0.0509

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

Approximate the logarithm to four decimal places using the change of base formula. - $\log _{1 / 5} 3$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $6 \log _ { b } x - \log _ { b } y$

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

Solve the equation. - $\log _ { 3 } ( 5 x + 3 ) = \log _ { 3 } ( 5 x + 7 )$

Solve the equation. - $3125 ^ { x } = \frac { 1 } { 625 }$

For the given functions f and g, find the requested function. - $f ( x ) = 6 x + 1 ; g ( x ) = 3 x - 5 \quad$ Find $\left( \frac { f } { g } \right) ( x )$

Solve the equation for x. Give an exact solution. - $\log x = 2.8$

For the given functions f and g, find the composition. - $f ( x ) = \sqrt { x + 5 } ; g ( x ) = 2 x \quad$ Find $( f \circ g ) ( 2 )$ .

Graph the function. - $y = \log _ { 1 / 2 } x$ $Graph the function. - y = \log _ { 1 / 2 } x$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 7 } 6 + \log _ { 7 } 13$

For the given functions f and g, find the requested function. -If $f ( x ) = 4 x ^ { 2 } + 6 x + 5$ and $g ( x ) = 6 x - 4$ , find $( g f ) ( x )$ .

Graph the exponential function. - $f(x)=\left(\frac{1}{5}\right)^{x+1}$ $Graph the exponential function. - f(x)=\left(\frac{1}{5}\right)^{x+1}$

For the given functions f and g, find the requested function. - $f ( x ) = x ^ { 2 } - 3 \sqrt [ 3 ] { x } ; g ( x ) = x - 5 \quad$ Find $\left( \frac { f } { g } \right) ( x )$

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x). - $h ( x ) = \left( 9 - 3 x ^ { 3 } \right) ^ { 2 }$

Use a calculator to approximate the logarithm to four decimal places. - $\log 4.60$

Use a calculator to approximate the logarithm to four decimal places. - $\log 0.0509$