Question 1

For the given functions f and g, find the composition.
-$$f ( x ) = \sqrt { x + 8 } ; g ( x ) = 8 x - 12$$
Find $( g \circ f ) ( x )$.

Accepted Answer

A)  $8 \sqrt { x + 8 } - 12$ 
B)  $2 \sqrt { 2 x - 1 }$ 
C)  $2 \sqrt { 2 x + 1 }$ 
D)  $8 \sqrt { x - 4 }$ 
A)  $8 \sqrt { x + 8 } - 12$ 
B)  $2 \sqrt { 2 x - 1 }$ 
C)  $2 \sqrt { 2 x + 1 }$ 
D)  $8 \sqrt { x - 4 }$

Question 2

Use the following approximations to find the approximate value of the logarithmic expression: $\log _ { b } 3 \approx 0.5$ logb $8 \approx 0.9$
$\log _ { b } 5 \approx 0.7$ logb $20 \approx 1.3$
-$\log _ { b } \sqrt { 5 }$ Round answer to nearest hundredth.

Accepted Answer

A)  $1.4$ 
B)  $0.84$ 
C)  $0.35$ 
D)  $2.24$ 
A)  $1.4$ 
B)  $0.84$ 
C)  $0.35$ 
D)  $2.24$

Question 3

Determine whether the functions f and g are inverses of each other.
-$$f ( x ) = x ^ { 3 } + 8 ; g ( x ) = \sqrt [ 3 ] { x - 8 }$$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 4

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$\log _ { 5 } 42 - \log _ { 5 } 6$

Accepted Answer

A)  $\log _ { 5 } 42$ 
B)  $\log _ { 5 } 7$ 
C)  $\log _ { 5 } 36$ 
D)  $\log _ { 5 } 252$ 
A)  $\log _ { 5 } 42$ 
B)  $\log _ { 5 } 7$ 
C)  $\log _ { 5 } 36$ 
D)  $\log _ { 5 } 252$

Question 5

Find the exact value.
-$\ln \sqrt [ 7 ] { \mathrm { e } }$

Accepted Answer

A)  $\frac { e } { 7 }$ 
B)  $7 \mathrm { e }$ 
C)  $\frac { 1 } { 7 }$ 
D)  7 
A)  $\frac { e } { 7 }$ 
B)  $7 \mathrm { e }$ 
C)  $\frac { 1 } { 7 }$ 
D)  7

Question 6

Solve.
-The formula $\mathrm { P } = 14.7 \mathrm { e } ^ { 0.21 \mathrm { x } }$ gives the average atmospheric pressure $\mathrm { P }$, in pounds per square inch, at an altitude $x$, in miles above sea level. Find the elevation of a jet if the atmospheric pressure outside the jet is $7.5$ pounds per square inch.

Accepted Answer

A)  $- 0.1$ miles 
B)  $- 3.2$ miles 
C)  $3.6$ miles 
D)  $71.0$ miles 
A)  $- 0.1$ miles 
B)  $- 3.2$ miles 
C)  $3.6$ miles 
D)  $71.0$ miles

Question 7

Write the function F(x) as a composition of f, g, or h.
-$$\begin{array} { l } 
f ( x ) = x ^ { 2 } - 3 \quad g ( x ) = 3 x \quad h ( x ) = \sqrt { x - 1 } \
F ( x ) = x - 4
\end{array}$$

Accepted Answer

A)  $F ( x ) = ( g \circ h ) ( x )$ 
B)  $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { g } ) ( \mathrm { x } )$ 
C)  $F ( x ) = ( f \circ g ) ( x )$ 
D)  $F ( x ) = ( f \circ h ) ( x )$ 
A)  $F ( x ) = ( g \circ h ) ( x )$ 
B)  $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { g } ) ( \mathrm { x } )$ 
C)  $F ( x ) = ( f \circ g ) ( x )$ 
D)  $F ( x ) = ( f \circ h ) ( x )$

Question 8

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. $$\begin{array} { l l l l } 
\text { inverse } & \text { common } & \text { composition symmetric } & \text { exponential } \
\text { vertical } & \text { logarithmic } & \text { natural half-life } & \text { horizontal }
\end{array}$$
-logarithms are logarithms to base 10.

Accepted Answer

A)  Exponential 
B)  Common 
C)  Inverse 
D)  Natural 
A)  Exponential 
B)  Common 
C)  Inverse 
D)  Natural

Question 9

Write as a logarithmic equation.
-$$7 ^ { 1 / 9 } = \sqrt [ 9 ] { 7 }$$

Accepted Answer

A)  $\log _ { 7 } \sqrt [ 9 ] { 7 } = \frac { 1 } { 9 }$ 
B)  $\log _ { 1 / 9 } \sqrt [ 9 ] { 7 } = 7$ 
C)  $\log _ { 1 / 9 } 7 = \sqrt [ 9 ] { 7 }$ 
D)  $\log _ { 7 } \frac { 1 } { 9 } = \sqrt [ 9 ] { 7 }$ 
A)  $\log _ { 7 } \sqrt [ 9 ] { 7 } = \frac { 1 } { 9 }$ 
B)  $\log _ { 1 / 9 } \sqrt [ 9 ] { 7 } = 7$ 
C)  $\log _ { 1 / 9 } 7 = \sqrt [ 9 ] { 7 }$ 
D)  $\log _ { 7 } \frac { 1 } { 9 } = \sqrt [ 9 ] { 7 }$

Question 10

Solve the equation.
-$$4 ^ { 2 x - 4 } = 8 ^ { 2 x }$$

Accepted Answer

A)  $\left\{ - \frac { 1 } { 4 } \right\}$ 
B)  $\{ 4 \}$ 
C)  $\left\{ \frac { 1 } { 4 } \right\}$ 
D)  $\{ - 4 \}$ 
A)  $\left\{ - \frac { 1 } { 4 } \right\}$ 
B)  $\{ 4 \}$ 
C)  $\left\{ \frac { 1 } { 4 } \right\}$ 
D)  $\{ - 4 \}$

Question 11

$f ( x ) = \sqrt { x } ; g ( x ) = x + 9$
Find $( f + g ) ( x )$

Accepted Answer

A)  $( f + g ) ( x ) = 9 \sqrt { x } + x$ 
B)  $( f + g ) ( x ) = x \sqrt { x } + 9$ 
C)  $( f + g ) ( x ) = \sqrt { x } + x + 9$ 
D)  $( f + g ) ( x ) = x \sqrt { x } + x ^ { 2 } + 9 x$ 
A)  $( f + g ) ( x ) = 9 \sqrt { x } + x$ 
B)  $( f + g ) ( x ) = x \sqrt { x } + 9$ 
C)  $( f + g ) ( x ) = \sqrt { x } + x + 9$ 
D)  $( f + g ) ( x ) = x \sqrt { x } + x ^ { 2 } + 9 x$

Question 12

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$\log _ { 9 } 6 + \log _ { 9 } 5 - \log _ { 9 } 10$

Accepted Answer

A)  $\log _ { 9 } \frac { 30 } { 10 }$ 
B)  $\log _ { 9 } 3$ 
C)  $\log _ { 9 } 1$ 
D)  $\log _ { 9 } \frac { 1 } { 3 }$ 
A)  $\log _ { 9 } \frac { 30 } { 10 }$ 
B)  $\log _ { 9 } 3$ 
C)  $\log _ { 9 } 1$ 
D)  $\log _ { 9 } \frac { 1 } { 3 }$

Question 13

Provide an appropriate response.
-If $\log _ { \mathrm { b } } 3 = 0.79$ and $\log _ { \mathrm { b } } 5 = 1.16$, find the value of of $\log _ { \mathrm { b } } \frac { 3 } { 125 }$.

Accepted Answer

A)  $- 2.69$ 
B)  $0.14$ 
C)  $- 1.11$ 
D)  $4.27$ 
A)  $- 2.69$ 
B)  $0.14$ 
C)  $- 1.11$ 
D)  $4.27$

Question 14

Solve.
-Four bacteria are placed in a petri dish. The population will double every day. The formula for the number of bacteria in the dish on day t is $$\mathrm { N } ( \mathrm { t } ) = 4 ( 2 ) ^ { \mathrm { t } }$$ where t is the number of days after the four bacteria are placed in the dish. How many bacteria are in the dish six
Days after the four bacteria are placed in the dish?

Accepted Answer

A)  144 
B)  256 
C)  12 
D)  48 
A)  144 
B)  256 
C)  12 
D)  48

Question 15

Solve the equation for x. Give an exact solution.
-$$\ln x = 2.4$$

Accepted Answer

A)  $\left\{ 10 ^ { 2.4 } \right\}$ 
B)  $\left\{ 2.4 ^ { 10 } \right\}$ 
C)  $\left\{ \mathrm { e } ^ { 2.4 } \right\}$ 
D)  $\{ 2.4 \mathrm { e } \}$ 
A)  $\left\{ 10 ^ { 2.4 } \right\}$ 
B)  $\left\{ 2.4 ^ { 10 } \right\}$ 
C)  $\left\{ \mathrm { e } ^ { 2.4 } \right\}$ 
D)  $\{ 2.4 \mathrm { e } \}$

Question 16

Use the formula A $$A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { or } A = P e ^ { r t } \text { to solve. }$$
-Find the amount in a n account in which $6000 is invested for 3 years at 9% interest compounded monthly.

Accepted Answer

A)  $7836.30 
B)  $6136.02 
C)  $6000 
D)  $7851.87 
A)  $7836.30 
B)  $6136.02 
C)  $6000 
D)  $7851.87

Question 17

Write as an exponential equation.
-$\log _ { 3 } 9 = 2$

Accepted Answer

A)  $2 ^ { 3 } = 9$ 
B)  $9 ^ { 2 } = 3$ 
C)  $3 ^ { 2 } = 9$ 
D)  $3 ^ { 9 } = 2$ 
A)  $2 ^ { 3 } = 9$ 
B)  $9 ^ { 2 } = 3$ 
C)  $3 ^ { 2 } = 9$ 
D)  $3 ^ { 9 } = 2$

Question 18

Decide whether the statement is true or false.
-$$\frac { \log _ { 10 } 5 } { \log _ { 10 } 10 } = \frac { 1 } { 2 }$$

Accepted Answer

A)  False 
B)  True 
A)  False 
B)  True

Question 19

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.
-$$\mathrm { f } = \{ ( - 5,1 ) , ( - 1,5 ) , ( - 7 , - 7 ) , ( 7,7 ) \}$$

Accepted Answer

A)  $f ^ { - 1 } = \{ ( 7 , - 7 ) , ( - 7 , - 1 ) , ( 1 , - 5 ) , ( - 7,7 ) \}$ 
B)  $\mathrm { f } ^ { - 1 } = \{ ( 1 , - 5 ) , ( 5 , - 1 ) , ( - 7 , - 7 ) , ( 7,7 ) \}$ 
C)  $f ^ { - 1 } = \{ ( 7 , - 7 ) , ( 5 , - 1 ) , ( 1 , - 1 ) , ( - 7,7 ) \}$ 
D)  not one-to-one 
A)  $f ^ { - 1 } = \{ ( 7 , - 7 ) , ( - 7 , - 1 ) , ( 1 , - 5 ) , ( - 7,7 ) \}$ 
B)  $\mathrm { f } ^ { - 1 } = \{ ( 1 , - 5 ) , ( 5 , - 1 ) , ( - 7 , - 7 ) , ( 7,7 ) \}$ 
C)  $f ^ { - 1 } = \{ ( 7 , - 7 ) , ( 5 , - 1 ) , ( 1 , - 1 ) , ( - 7,7 ) \}$ 
D)  not one-to-one

Question 20

Use the properties of logarithms to write the expression as a single logarithm.
-$$\log _ { 3 } 6 + \log _ { 3 } 5$$

Accepted Answer

A)  $\log _ { 3 } 30$ 
B)  $\log _ { 30 } 3$ 
C)  $\log _ { 3 } 11$ 
D)  $\log _ { 3 } \frac { 6 } { 5 }$ 
A)  $\log _ { 3 } 30$ 
B)  $\log _ { 30 } 3$ 
C)  $\log _ { 3 } 11$ 
D)  $\log _ { 3 } \frac { 6 } { 5 }$

For the given functions f and g, find the composition. - $f ( x ) = \sqrt { x + 8 } ; g ( x ) = 8 x - 12$ Find $( g \circ f ) ( x )$ .

Use the following approximations to find the approximate value of the logarithmic expression: $\log _ { b } 3 \approx 0.5$ logb $8 \approx 0.9$ $\log _ { b } 5 \approx 0.7$ logb $20 \approx 1.3$ - $\log _ { b } \sqrt { 5 }$ Round answer to nearest hundredth.

Determine whether the functions f and g are inverses of each other. - $f ( x ) = x ^ { 3 } + 8 ; g ( x ) = \sqrt [ 3 ] { x - 8 }$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 5 } 42 - \log _ { 5 } 6$

Find the exact value. - $\ln \sqrt [ 7 ] { \mathrm { e } }$

Write the function F(x) as a composition of f, g, or h. - f(x)=-3g(x)=3xh(x)= F(x)=x-4

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. inverse common composition symmetric exponential vertical logarithmic natural half-life horizontal -logarithms are logarithms to base 10.

Write as a logarithmic equation. - $7 ^ { 1 / 9 } = \sqrt [ 9 ] { 7 }$

Solve the equation. - $4 ^ { 2 x - 4 } = 8 ^ { 2 x }$

$f ( x ) = \sqrt { x } ; g ( x ) = x + 9$ Find $( f + g ) ( x )$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 9 } 6 + \log _ { 9 } 5 - \log _ { 9 } 10$

Provide an appropriate response. -If $\log _ { \mathrm { b } } 3 = 0.79$ and $\log _ { \mathrm { b } } 5 = 1.16$ , find the value of of $\log _ { \mathrm { b } } \frac { 3 } { 125 }$ .

Solve the equation for x. Give an exact solution. - $\ln x = 2.4$

Use the formula A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { or } A = P e ^ { r t } \text { to solve. }$ -Find the amount in a n account in which $6000 is invested for 3 years at 9% interest compounded monthly.

Write as an exponential equation. - $\log _ { 3 } 9 = 2$

Decide whether the statement is true or false. - $\frac { \log _ { 10 } 5 } { \log _ { 10 } 10 } = \frac { 1 } { 2 }$

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. - $\mathrm { f } = \{ ( - 5,1 ) , ( - 1,5 ) , ( - 7 , - 7 ) , ( 7,7 ) \}$

Use the properties of logarithms to write the expression as a single logarithm. - $\log _ { 3 } 6 + \log _ { 3 } 5$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Fractions

Filters

Exam 9: Exponential and Logarithmic Functions

For the given functions f and g, find the composition. - f(x)=x+8;g(x)=8x−12f ( x ) = \sqrt { x + 8 } ; g ( x ) = 8 x - 12f(x)=x+8​;g(x)=8x−12 Find (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) .

Determine whether the functions f and g are inverses of each other. - f(x)=x3+8;g(x)=x−83f ( x ) = x ^ { 3 } + 8 ; g ( x ) = \sqrt [ 3 ] { x - 8 }f(x)=x3+8;g(x)=3x−8​

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - log⁡542−log⁡56\log _ { 5 } 42 - \log _ { 5 } 6log5​42−log5​6

Find the exact value. - ln⁡e7\ln \sqrt [ 7 ] { \mathrm { e } }ln7e​