Question 1

Evaluate the function $f ( x ) = \log _ { 2 } x$ at $x = \frac { 1 } { 2 }$ without using a calculator.

Accepted Answer

A)  0 
B)  $- 1$ 
C)  $- 2$ 
D)  2 
E)  $\frac { 1 } { 2 }$ 
A)  0 
B)  $- 1$ 
C)  $- 2$ 
D)  2 
E)  $\frac { 1 } { 2 }$

Question 2

Solve the logarithmic equation below algebraically. Round your result to three decimal places.
$$4 \log _ { 3 } ( x - 4 ) = 13$$

Accepted Answer

A)  $41.280$ 
B)  $43.869$ 
C)  $43.623$ 
D)  $35.658$ 
E)  $39.534$ 
A)  $41.280$ 
B)  $43.869$ 
C)  $43.623$ 
D)  $35.658$ 
E)  $39.534$

Question 3

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
$\ln \sqrt [ 6 ] { t }$

Accepted Answer

A)  $\frac { 1 } { 6 } \ln t$ 
B)  $\ln t - \frac { 1 } { 6 }$ 
C)  $\ln t - 6$ 
D)  $\frac { 1 } { 3 } \ln t$ 
E)  $\ln t - \frac { 1 } { 3 }$ 
A)  $\frac { 1 } { 6 } \ln t$ 
B)  $\ln t - \frac { 1 } { 6 }$ 
C)  $\ln t - 6$ 
D)  $\frac { 1 } { 3 } \ln t$ 
E)  $\ln t - \frac { 1 } { 3 }$

Question 4

Solve the exponential equation below algebraically. Round your result to three decimal places.
$$\frac { 375 } { 1 + e ^ { x } } = 125$$

Accepted Answer

A)  $2.697$ 
B)  $2.883$ 
C)  $3.303$ 
D)  $- 1.086$ 
E)  $0.693$ 
A)  $2.697$ 
B)  $2.883$ 
C)  $3.303$ 
D)  $- 1.086$ 
E)  $0.693$

Question 5

Match the function $y = \frac { 3 } { 1 + e ^ { - 2 x } }$ with its graph.
Graph I:
 
Graph II:
 
Graph III:
 
Graph IV:
 
 Graph V:

Accepted Answer

A)  Graph V 
B)  Graph II 
C)  Graph I 
D)  Graph III 
E)  Graph IV 
A)  Graph V 
B)  Graph II 
C)  Graph I 
D)  Graph III 
E)  Graph IV

Question 6

Solve the logarithmic equation below algebraically. Round your result to three decimal places.
$1 + 2 \ln x = 6$

Accepted Answer

A)  $8.318$ 
B)  $10.682$ 
C)  $12.182$ 
D)  $15.377$ 
E)  $11.366$ 
A)  $8.318$ 
B)  $10.682$ 
C)  $12.182$ 
D)  $15.377$ 
E)  $11.366$

Question 7

Rewrite the logarithm $\log _ { 4 } 25$ in terms of the natural logarithm.

Accepted Answer

A)  $\frac { \ln 25 } { \ln 4 }$ 
B)  $\frac { \ln 4 } { \ln 25 }$ 
C)  $\ln 4 \ln 25$ 
D)  $\frac { \ln 25 } { \log _ { 4 } e }$ 
E)  $\ln 25$ 
A)  $\frac { \ln 25 } { \ln 4 }$ 
B)  $\frac { \ln 4 } { \ln 25 }$ 
C)  $\ln 4 \ln 25$ 
D)  $\frac { \ln 25 } { \log _ { 4 } e }$ 
E)  $\ln 25$

Question 8

Determine whether the scatter plot below could best be modeled by a linear model, a quadratic model, an exponential model, a logarithmic model, or a logistic model.

Accepted Answer

A)  a logistic model 
B)  an exponential model 
C)  a linear model 
D)  a logarithmic model 
E)  a quadratic model 
A)  a logistic model 
B)  an exponential model 
C)  a linear model 
D)  a logarithmic model 
E)  a quadratic model

Question 9

Rewrite the logarithm $\log _ { 4 } 25$ in terms of the natural logarithm.

Accepted Answer

A)  $\frac { \ln 25 } { \ln 4 }$ 
B)  $\frac { \ln 4 } { \ln 25 }$ 
C)  $\ln 4 \ln 25$ 
D)  $\frac { \ln 25 } { \log _ { 4 } e }$ 
E)  $\ln 25$ 
A)  $\frac { \ln 25 } { \ln 4 }$ 
B)  $\frac { \ln 4 } { \ln 25 }$ 
C)  $\ln 4 \ln 25$ 
D)  $\frac { \ln 25 } { \log _ { 4 } e }$ 
E)  $\ln 25$

Question 10

Determine whether the scatter plot below could best be modeled by a linear model, a quadratic model, an exponential model, a logarithmic model, or a logistic model.

Accepted Answer

A)  a linear model 
B)  a quadratic model 
C)  a logistic model 
D)  an exponential model 
E)  a logarithmic model 
A)  a linear model 
B)  a quadratic model 
C)  a logistic model 
D)  an exponential model 
E)  a logarithmic model

Question 11

Evaluate the function $f ( x ) = \log _ { 4 } x$ at $x = \frac { 1 } { 64 }$ without using a calculator.

Accepted Answer

A)  $- 2$ 
B)  $- 3$ 
C)  $- 4$ 
D)  64 
E)  $\frac { 1 } { 64 }$ 
A)  $- 2$ 
B)  $- 3$ 
C)  $- 4$ 
D)  64 
E)  $\frac { 1 } { 64 }$

Question 12

Solve the exponential equation below algebraically. Round your result to three decimal places.
$$e ^ { 2 x } + 3 e ^ { x } - 18 = 0$$

Accepted Answer

A)  $1.099$ 
B)  $0.214$ 
C)  $2.077$ 
D)  $- 0.188$ 
E)  $3.271$ 
A)  $1.099$ 
B)  $0.214$ 
C)  $2.077$ 
D)  $- 0.188$ 
E)  $3.271$

Question 13

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
$\log _ { 4 } \frac { y } { 2 }$

Accepted Answer

A)  $2 \log _ { 4 } y$ 
B)  $y - \log _ { 4 } 2$ 
C)  $\log _ { 4 } y - 2$ 
D)  $\frac { \log _ { 4 } y } { 2 }$ 
E)  $\log _ { 4 } y - \log _ { 4 } 2$ 
A)  $2 \log _ { 4 } y$ 
B)  $y - \log _ { 4 } 2$ 
C)  $\log _ { 4 } y - 2$ 
D)  $\frac { \log _ { 4 } y } { 2 }$ 
E)  $\log _ { 4 } y - \log _ { 4 } 2$

Question 14

Rewrite the logarithmic equation $\log _ { 4 } \frac { 1 } { 16 } = - 2$ in exponential form.

Accepted Answer

A)  $4 ^ { 16 } = - 2$ 
B)  $4 ^ { 1 / 16 } = - 2$ 
C)  $4 ^ { - 2 } = \frac { 1 } { 16 }$ 
D)  $\left( \frac { 1 } { 16 } \right) ^ { - 2 } = 4$ 
E)  $4 ^ { - 2 } = - \frac { 1 } { 16 }$ 
A)  $4 ^ { 16 } = - 2$ 
B)  $4 ^ { 1 / 16 } = - 2$ 
C)  $4 ^ { - 2 } = \frac { 1 } { 16 }$ 
D)  $\left( \frac { 1 } { 16 } \right) ^ { - 2 } = 4$ 
E)  $4 ^ { - 2 } = - \frac { 1 } { 16 }$

Question 15

Determine whether or not $x = \frac { 1 } { 3 } \left( e ^ { - 2 } + 1 \right)$ is a solution to $\ln ( 3 x - 1 ) = - 2$.

Accepted Answer

A)  yes 
B)  no 
A)  yes 
B)  no

Question 16

Solve the equation below algebraically.
$$- 2 x ^ { 2 } e ^ { 4 x } - 16 x e ^ { 4 x } = 0$$

Accepted Answer

A)  $- 8$ and 4 
B)  4 and 5 
C)  $- 8$ and 5 
D)  0 and 5 
E)  $- 8$ and 0 
A)  $- 8$ and 4 
B)  4 and 5 
C)  $- 8$ and 5 
D)  0 and 5 
E)  $- 8$ and 0

Question 17

What is the value of the function $f ( x ) = 3.3 e ^ { - 1.8 x }$ at $x = 2.5 ?$ Round to 3 decimal places.

Accepted Answer

A)  $0.545$ 
B)  $0.037$ 
C)  $\quad 6.645$ 
D)  $- 40.366$ 
E)  $0.000$ 
A)  $0.545$ 
B)  $0.037$ 
C)  $\quad 6.645$ 
D)  $- 40.366$ 
E)  $0.000$

Question 18

Solve $\ln x ^ { 2 } = 13$ for $x$.

Accepted Answer

A)  $e ^ { 169 }$ 
B)  $10 ^ { \sqrt { 3 } }$ 
C)  $e ^ { \sqrt { 13 } }$ 
D)  $- e ^ { 13 / 2 } , e ^ { 13 / 2 }$ 
E)  no solution 
A)  $e ^ { 169 }$ 
B)  $10 ^ { \sqrt { 3 } }$ 
C)  $e ^ { \sqrt { 13 } }$ 
D)  $- e ^ { 13 / 2 } , e ^ { 13 / 2 }$ 
E)  no solution

Question 19

Solve the exponential equation below algebraically. Round your result to three decimal places.
$$150 e ^ { - 0.01 x } = 140,000$$

Accepted Answer

A)  $- 704.498$ 
B)  $- 695.069$ 
C)  $- 682.289$ 
D)  $- 683.876$ 
E)  $- 707.153$ 
A)  $- 704.498$ 
B)  $- 695.069$ 
C)  $- 682.289$ 
D)  $- 683.876$ 
E)  $- 707.153$

Question 20

Rewrite the logarithmic equation $\log _ { 2 } \frac { 1 } { 4 } = - 2$ in exponential form.

Accepted Answer

A)  $2 ^ { 4 } = - 2$ 
B)  $2 ^ { 1 / 4 } = - 2$ 
C)  $2 ^ { - 2 } = \frac { 1 } { 4 }$ 
D)  $\left( \frac { 1 } { 4 } \right) ^ { - 2 } = 2$ 
E)  $2 ^ { - 2 } = - \frac { 1 } { 4 }$ 
A)  $2 ^ { 4 } = - 2$ 
B)  $2 ^ { 1 / 4 } = - 2$ 
C)  $2 ^ { - 2 } = \frac { 1 } { 4 }$ 
D)  $\left( \frac { 1 } { 4 } \right) ^ { - 2 } = 2$ 
E)  $2 ^ { - 2 } = - \frac { 1 } { 4 }$

Evaluate the function $f ( x ) = \log _ { 2 } x$ at $x = \frac { 1 } { 2 }$ without using a calculator.

Solve the logarithmic equation below algebraically. Round your result to three decimal places. $4 \log _ { 3 } ( x - 4 ) = 13$

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $\ln \sqrt [ 6 ] { t }$

Solve the exponential equation below algebraically. Round your result to three decimal places. $\frac { 375 } { 1 + e ^ { x } } = 125$

Solve the logarithmic equation below algebraically. Round your result to three decimal places. $1 + 2 \ln x = 6$

Rewrite the logarithm $\log _ { 4 } 25$ in terms of the natural logarithm.

Determine whether the scatter plot below could best be modeled by a linear model, a quadratic model, an exponential model, a logarithmic model, or a logistic model.

Rewrite the logarithm $\log _ { 4 } 25$ in terms of the natural logarithm.

Determine whether the scatter plot below could best be modeled by a linear model, a quadratic model, an exponential model, a logarithmic model, or a logistic model.

Evaluate the function $f ( x ) = \log _ { 4 } x$ at $x = \frac { 1 } { 64 }$ without using a calculator.

Solve the exponential equation below algebraically. Round your result to three decimal places. $e ^ { 2 x } + 3 e ^ { x } - 18 = 0$

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $\log _ { 4 } \frac { y } { 2 }$

Rewrite the logarithmic equation $\log _ { 4 } \frac { 1 } { 16 } = - 2$ in exponential form.

Determine whether or not $x = \frac { 1 } { 3 } \left( e ^ { - 2 } + 1 \right)$ is a solution to $\ln ( 3 x - 1 ) = - 2$ .

Solve the equation below algebraically. $- 2 x ^ { 2 } e ^ { 4 x } - 16 x e ^ { 4 x } = 0$

What is the value of the function $f ( x ) = 3.3 e ^ { - 1.8 x }$ at $x = 2.5 ?$ Round to 3 decimal places.

Solve $\ln x ^ { 2 } = 13$ for $x$ .

Solve the exponential equation below algebraically. Round your result to three decimal places. $150 e ^ { - 0.01 x } = 140,000$

Rewrite the logarithmic equation $\log _ { 2 } \frac { 1 } { 4 } = - 2$ in exponential form.

Functions and Their Graphs

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Filters

Exam 3: Exponential and Logarithmic Functions

Evaluate the function f(x)=log⁡2xf ( x ) = \log _ { 2 } xf(x)=log2​x at x=12x = \frac { 1 } { 2 }x=21​ without using a calculator.

Solve the logarithmic equation below algebraically. Round your result to three decimal places. 4log⁡3(x−4)=134 \log _ { 3 } ( x - 4 ) = 134log3​(x−4)=13

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) ln⁡t6\ln \sqrt [ 6 ] { t }ln6t​

Solve the exponential equation below algebraically. Round your result to three decimal places. 3751+ex=125\frac { 375 } { 1 + e ^ { x } } = 1251+ex375​=125

Match the function y=31+e−2xy = \frac { 3 } { 1 + e ^ { - 2 x } }y=1+e−2x3​ with its graph. Graph I: Graph II: Graph III: Graph IV: Graph V:

Solve the logarithmic equation below algebraically. Round your result to three decimal places. 1+2ln⁡x=61 + 2 \ln x = 61+2lnx=6

Rewrite the logarithm log⁡425\log _ { 4 } 25log4​25 in terms of the natural logarithm.

Determine whether the scatter plot below could best be modeled by a linear model, a quadratic model, an exponential model, a logarithmic model, or a logistic model.

Rewrite the logarithm log⁡425\log _ { 4 } 25log4​25 in terms of the natural logarithm.

Determine whether the scatter plot below could best be modeled by a linear model, a quadratic model, an exponential model, a logarithmic model, or a logistic model.

Evaluate the function f(x)=log⁡4xf ( x ) = \log _ { 4 } xf(x)=log4​x at x=164x = \frac { 1 } { 64 }x=641​ without using a calculator.

Solve the exponential equation below algebraically. Round your result to three decimal places. e2x+3ex−18=0e ^ { 2 x } + 3 e ^ { x } - 18 = 0e2x+3ex−18=0

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) log⁡4y2\log _ { 4 } \frac { y } { 2 }log4​2y​

Rewrite the logarithmic equation log⁡4116=−2\log _ { 4 } \frac { 1 } { 16 } = - 2log4​161​=−2 in exponential form.

Determine whether or not x=13(e−2+1)x = \frac { 1 } { 3 } \left( e ^ { - 2 } + 1 \right)x=31​(e−2+1) is a solution to ln⁡(3x−1)=−2\ln ( 3 x - 1 ) = - 2ln(3x−1)=−2 .

Solve the equation below algebraically. −2x2e4x−16xe4x=0- 2 x ^ { 2 } e ^ { 4 x } - 16 x e ^ { 4 x } = 0−2x2e4x−16xe4x=0

What is the value of the function f(x)=3.3e−1.8xf ( x ) = 3.3 e ^ { - 1.8 x }f(x)=3.3e−1.8x at x=2.5?x = 2.5 ?x=2.5? Round to 3 decimal places.

Solve ln⁡x2=13\ln x ^ { 2 } = 13lnx2=13 for xxx .

Solve the exponential equation below algebraically. Round your result to three decimal places. 150e−0.01x=140,000150 e ^ { - 0.01 x } = 140,000150e−0.01x=140,000

Rewrite the logarithmic equation log⁡214=−2\log _ { 2 } \frac { 1 } { 4 } = - 2log2​41​=−2 in exponential form.

Functions and Their Graphs

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Filters

Evaluate the function $f ( x ) = \log _ { 2 } x$ at $x = \frac { 1 } { 2 }$ without using a calculator.

Solve the logarithmic equation below algebraically. Round your result to three decimal places. $4 \log _ { 3 } ( x - 4 ) = 13$

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $\ln \sqrt [ 6 ] { t }$

Solve the exponential equation below algebraically. Round your result to three decimal places. $\frac { 375 } { 1 + e ^ { x } } = 125$

Solve the logarithmic equation below algebraically. Round your result to three decimal places. $1 + 2 \ln x = 6$

Rewrite the logarithm $\log _ { 4 } 25$ in terms of the natural logarithm.

Rewrite the logarithm $\log _ { 4 } 25$ in terms of the natural logarithm.

Evaluate the function $f ( x ) = \log _ { 4 } x$ at $x = \frac { 1 } { 64 }$ without using a calculator.

Solve the exponential equation below algebraically. Round your result to three decimal places. $e ^ { 2 x } + 3 e ^ { x } - 18 = 0$

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $\log _ { 4 } \frac { y } { 2 }$

Rewrite the logarithmic equation $\log _ { 4 } \frac { 1 } { 16 } = - 2$ in exponential form.

Determine whether or not $x = \frac { 1 } { 3 } \left( e ^ { - 2 } + 1 \right)$ is a solution to $\ln ( 3 x - 1 ) = - 2$ .

Solve the equation below algebraically. $- 2 x ^ { 2 } e ^ { 4 x } - 16 x e ^ { 4 x } = 0$

What is the value of the function $f ( x ) = 3.3 e ^ { - 1.8 x }$ at $x = 2.5 ?$ Round to 3 decimal places.

Solve $\ln x ^ { 2 } = 13$ for $x$ .

Solve the exponential equation below algebraically. Round your result to three decimal places. $150 e ^ { - 0.01 x } = 140,000$

Rewrite the logarithmic equation $\log _ { 2 } \frac { 1 } { 4 } = - 2$ in exponential form.