Question 1

Evaluate the expression without using a calculator.
-$\log _ { 8 } 8 ^ { 20 }$

Accepted Answer

A)  $\log _ { 8 } 20$ 
B)  20 
C)  28 
D)  8 
A)  $\log _ { 8 } 20$ 
B)  20 
C)  28 
D)  8

Question 2

Solve the problem.
-Use the formula $R = \log \left( \frac { \mathrm { a } } { \mathrm { T } } \right) + \mathrm { B }$ to find the intensity $\mathrm { R }$ on the Richter scale, given that amplitude a is 444 micrometers, time T between waves is 3 seconds, and B is 3 . Round answer to one decimal place.

Accepted Answer

A)  $2.2$ 
B)  8 
C)  $8.5$ 
D)  $5.2$ 
A)  $2.2$ 
B)  8 
C)  $8.5$ 
D)  $5.2$

Question 3

$$\text { Use the compound interest formulas } A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
-Find the accumulated value of an investment of $10,000 at 4% compounded semiannually for 5 years.

Accepted Answer

A) $12,000.00 
B) $11,040.81 
C) $12,166.53 
D) $12,189.94 
A) $12,000.00 
B) $11,040.81 
C) $12,166.53 
D) $12,189.94

Question 4

$$\text { Use the compound interest formulas } A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
-Find the accumulated value of an investment of $5000 at 5% compounded monthly for 8 years.

Accepted Answer

A) $9093.60 
B) $8060.16 
C) $12,911.25 
D) $7452.93 
A) $9093.60 
B) $8060.16 
C) $12,911.25 
D) $7452.93

Question 5

Graph the function.
-Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = e ^ { 3 x }$.

Accepted Answer

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

Question 6

Graph the function.
-Use the graph of $f ( x ) = 3 ^ { x }$ to obtain the graph of $g ( x ) = 3 ^ { x } - 1$.

Accepted Answer

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

Question 7

Find the domain of the logarithmic function.
-$$f ( x ) = \log \left( \frac { x + 9 } { x - 4 } \right)$$

Accepted Answer

A)  $( - \infty , - 9 )$ 
B)  $( 4 , \infty )$ 
C)  $( - \infty , - 9 ) \cup ( 4 , \infty )$ 
D)  $( - 9,4 )$ 
A)  $( - \infty , - 9 )$ 
B)  $( 4 , \infty )$ 
C)  $( - \infty , - 9 ) \cup ( 4 , \infty )$ 
D)  $( - 9,4 )$

Question 8

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$$\log _ { 7 } x ^ { 6 }$$

Accepted Answer

A)  $7 \log _ { 6 } x$ 
B)  $7 \log x$ 
C)  $6 \log _ { 7 } x ^ { 6 }$ 
D)  $6 \log _ { 7 } x$ 
A)  $7 \log _ { 6 } x$ 
B)  $7 \log x$ 
C)  $6 \log _ { 7 } x ^ { 6 }$ 
D)  $6 \log _ { 7 } x$

Question 9

$$\text { Use the compound interest formulas } A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
-Suppose that you have $10,000 to invest. Which investment yields the greater return over 6 years: 8.75% compounded continuously or 8.9% compounded semiannually?

Accepted Answer

A) $10,000 invested at 8.75% compounded continuously over 6 years yields the greater return. 
B) Both investment plans yield the same return. 
C) $10,000 invested at 8.9% compounded semiannually over 6 years yields the greater return. 
A) $10,000 invested at 8.75% compounded continuously over 6 years yields the greater return. 
B) Both investment plans yield the same return. 
C) $10,000 invested at 8.9% compounded semiannually over 6 years yields the greater return.

Question 10

Evaluate the expression without using a calculator.
-$\log _ { 9 } 81$

Accepted Answer

A)  9 
B)  81 
C)  18 
D)  2 
A)  9 
B)  81 
C)  18 
D)  2

Question 11

The graph of an exponential function is given. Select the function for the graph from the functions listed.
-

Accepted Answer

A)  $f ( x ) = - 5 ^ { x }$ 
B)  $f ( x ) = 5 ^ { - x }$ 
C)  $f ( x ) = - 5 ^ { - x }$ 
D)  $f ( x ) = 5 ^ { x }$ 
A)  $f ( x ) = - 5 ^ { x }$ 
B)  $f ( x ) = 5 ^ { - x }$ 
C)  $f ( x ) = - 5 ^ { - x }$ 
D)  $f ( x ) = 5 ^ { x }$

Question 12

The graph of an exponential function is given. Select the function for the graph from the functions listed.
-

Accepted Answer

A)  $f ( x ) = 3 ^ { x } + 1$ 
B)  $f ( x ) = 3 ^ { x }$ 
C)  $f ( x ) = 3 ^ { x } - 1$ 
D)  $f ( x ) = 3 ^ { x - 1 }$ 
A)  $f ( x ) = 3 ^ { x } + 1$ 
B)  $f ( x ) = 3 ^ { x }$ 
C)  $f ( x ) = 3 ^ { x } - 1$ 
D)  $f ( x ) = 3 ^ { x - 1 }$

Question 13

Write the equation in its equivalent logarithmic form.
-$12 ^ { 3 } = y$

Accepted Answer

A)  $\log _ { 3 } y = 12$ 
B)  $\log _ { 12 } y = 3$ 
C)  $\log _ { y } 3 = 12$ 
D)  $\log _ { y } 12 = 3$ 
A)  $\log _ { 3 } y = 12$ 
B)  $\log _ { 12 } y = 3$ 
C)  $\log _ { y } 3 = 12$ 
D)  $\log _ { y } 12 = 3$

Question 14

Evaluate the expression without using a calculator.
-$\log _ { 4 } 1$

Accepted Answer

A)  1 
B)  $\frac { 1 } { 4 }$ 
C)  4 
D)  0 
A)  1 
B)  $\frac { 1 } { 4 }$ 
C)  4 
D)  0

Question 15

Solve the problem.
-The formula $S = A \left( \frac { ( 1 + r ) ^ { t + 1 } - 1 } { r } \right)$ models the value of a retirement account, where $A =$ the number of dollars added to the retirement account each year, $r =$ the annual interest rate, and $\mathrm { S } =$ the value of the retirement iccount after t years. If the interest rate is $6 \%$, how much will the account be worth after 10 years if $\$ 1600$ is added each year? Round to the nearest whole number.

Accepted Answer

A)  $\$ 23,955$ 
B)  $\$ 31,519$ 
C)  $\$ 3021$ 
D)  $\$ 17,600$ 
A)  $\$ 23,955$ 
B)  $\$ 31,519$ 
C)  $\$ 3021$ 
D)  $\$ 17,600$

Question 16

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 6 } \left( \frac { x - 6 } { x ^ { 8 } } \right)$

Accepted Answer

A)  $\log _ { 6 } ( x - 6 ) - \log _ { 6 } x$ 
B)  $8 \log _ { 6 } x - \log _ { 6 } ( x - 6 )$ 
C)  $\log _ { 6 } ( x - 6 ) + 8 \log _ { 6 } x$ 
D)  $\log _ { 6 } ( x - 6 ) - 8 \log _ { 6 } x$ 
A)  $\log _ { 6 } ( x - 6 ) - \log _ { 6 } x$ 
B)  $8 \log _ { 6 } x - \log _ { 6 } ( x - 6 )$ 
C)  $\log _ { 6 } ( x - 6 ) + 8 \log _ { 6 } x$ 
D)  $\log _ { 6 } ( x - 6 ) - 8 \log _ { 6 } x$

Question 17

Graph the functions in the same rectangular coordinate system.
-$$f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x } \text { and } g ( x ) = \log _ { 1 / 4 } x$$

Accepted Answer

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

Question 18

$$\text { Use the compound interest formulas } A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
-Find the accumulated value of an investment of $3000 at 8% compounded annually for 9 years.

Accepted Answer

A) $5552.79 
B) $4920.00 
C) $5997.01 
D) $5160.00 
A) $5552.79 
B) $4920.00 
C) $5997.01 
D) $5160.00

Question 19

Graph the function.
-Use the graph of $\log _ { 4 } x$ to obtain the graph of $f ( x ) = \log _ { 4 } ( x + 1 )$.

Accepted Answer

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

Question 20

Evaluate or simplify the expression without using a calculator.
-$9 \left( 10 \log ^ { 5.4 } \right)$

Accepted Answer

A)  $15.1776$ 
B)  $4.86$ 
C)  $48.6$ 
D)  486 
A)  $15.1776$ 
B)  $4.86$ 
C)  $48.6$ 
D)  486

Evaluate the expression without using a calculator. - $\log _ { 8 } 8 ^ { 20 }$

$\text { Use the compound interest formulas } A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$ -Find the accumulated value of an investment of $10,000 at 4% compounded semiannually for 5 years.

$\text { Use the compound interest formulas } A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$ -Find the accumulated value of an investment of $5000 at 5% compounded monthly for 8 years.

Graph the function. -Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = e ^ { 3 x }$ . $Graph the function. -Use the graph of f ( x ) = e ^ { x } to obtain the graph of g ( x ) = e ^ { 3 x } .$

Graph the function. -Use the graph of $f ( x ) = 3 ^ { x }$ to obtain the graph of $g ( x ) = 3 ^ { x } - 1$ . $Graph the function. -Use the graph of f ( x ) = 3 ^ { x } to obtain the graph of g ( x ) = 3 ^ { x } - 1 .$

Find the domain of the logarithmic function. - $f ( x ) = \log \left( \frac { x + 9 } { x - 4 } \right)$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 7 } x ^ { 6 }$

Evaluate the expression without using a calculator. - $\log _ { 9 } 81$

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Write the equation in its equivalent logarithmic form. - $12 ^ { 3 } = y$

Evaluate the expression without using a calculator. - $\log _ { 4 } 1$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 6 } \left( \frac { x - 6 } { x ^ { 8 } } \right)$

$\text { Use the compound interest formulas } A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$ -Find the accumulated value of an investment of $3000 at 8% compounded annually for 9 years.

Graph the function. -Use the graph of $\log _ { 4 } x$ to obtain the graph of $f ( x ) = \log _ { 4 } ( x + 1 )$ . $Graph the function. -Use the graph of \log _ { 4 } x to obtain the graph of f ( x ) = \log _ { 4 } ( x + 1 ) .$

Evaluate or simplify the expression without using a calculator. - $9 \left( 10 \log ^ { 5.4 } \right)$

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Systems of Equations and Inequalities

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Exam 4: Exponential and Logarithmic Functions

Evaluate the expression without using a calculator. - log⁡8820\log _ { 8 } 8 ^ { 20 }log8​820

Graph the function. -Use the graph of f(x)=exf ( x ) = e ^ { x }f(x)=ex to obtain the graph of g(x)=e3xg ( x ) = e ^ { 3 x }g(x)=e3x .

Graph the function. -Use the graph of f(x)=3xf ( x ) = 3 ^ { x }f(x)=3x to obtain the graph of g(x)=3x−1g ( x ) = 3 ^ { x } - 1g(x)=3x−1 .

Find the domain of the logarithmic function. - f(x)=log⁡(x+9x−4)f ( x ) = \log \left( \frac { x + 9 } { x - 4 } \right)f(x)=log(x−4x+9​)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡7x6\log _ { 7 } x ^ { 6 }log7​x6

Evaluate the expression without using a calculator. - log⁡981\log _ { 9 } 81log9​81

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Write the equation in its equivalent logarithmic form. - 123=y12 ^ { 3 } = y123=y

Evaluate the expression without using a calculator. - log⁡41\log _ { 4 } 1log4​1

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡6(x−6x8)\log _ { 6 } \left( \frac { x - 6 } { x ^ { 8 } } \right)log6​(x8x−6​)

Graph the functions in the same rectangular coordinate system. - f(x)=(14)x and g(x)=log⁡1/4xf ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x } \text { and } g ( x ) = \log _ { 1 / 4 } xf(x)=(41​)x and g(x)=log1/4​x

Graph the function. -Use the graph of log⁡4x\log _ { 4 } xlog4​x to obtain the graph of f(x)=log⁡4(x+1)f ( x ) = \log _ { 4 } ( x + 1 )f(x)=log4​(x+1) .

Evaluate or simplify the expression without using a calculator. - 9(10log⁡5.4)9 \left( 10 \log ^ { 5.4 } \right)9(10log5.4)

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Systems of Equations and Inequalities

Filters

Evaluate the expression without using a calculator. - $\log _ { 8 } 8 ^ { 20 }$

Graph the function. -Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = e ^ { 3 x }$ . $Graph the function. -Use the graph of f ( x ) = e ^ { x } to obtain the graph of g ( x ) = e ^ { 3 x } .$

Graph the function. -Use the graph of $f ( x ) = 3 ^ { x }$ to obtain the graph of $g ( x ) = 3 ^ { x } - 1$ . $Graph the function. -Use the graph of f ( x ) = 3 ^ { x } to obtain the graph of g ( x ) = 3 ^ { x } - 1 .$

Find the domain of the logarithmic function. - $f ( x ) = \log \left( \frac { x + 9 } { x - 4 } \right)$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 7 } x ^ { 6 }$

Evaluate the expression without using a calculator. - $\log _ { 9 } 81$

Write the equation in its equivalent logarithmic form. - $12 ^ { 3 } = y$

Evaluate the expression without using a calculator. - $\log _ { 4 } 1$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 6 } \left( \frac { x - 6 } { x ^ { 8 } } \right)$

Graph the function. -Use the graph of $\log _ { 4 } x$ to obtain the graph of $f ( x ) = \log _ { 4 } ( x + 1 )$ . $Graph the function. -Use the graph of \log _ { 4 } x to obtain the graph of f ( x ) = \log _ { 4 } ( x + 1 ) .$

Evaluate or simplify the expression without using a calculator. - $9 \left( 10 \log ^ { 5.4 } \right)$