Question 1

Solve the equation for $c$.
-$(3 \mathrm{p}+9)=\ln (2 \mathrm{c})+\ln \mathrm{c}$

Accepted Answer

A)  $\sqrt{\frac{3 p+9}{2}}$ 
B)  $\sqrt{\frac{e^{3 p+9}}{2}}$ 
C)  $\sqrt{\frac{\mathrm{e}^{3}+\mathrm{e}^{\mathrm{p}+9}}{2}}$ 
D)  $\sqrt{e^{3 p+9}}$ 
A)  $\sqrt{\frac{3 p+9}{2}}$ 
B)  $\sqrt{\frac{e^{3 p+9}}{2}}$ 
C)  $\sqrt{\frac{\mathrm{e}^{3}+\mathrm{e}^{\mathrm{p}+9}}{2}}$ 
D)  $\sqrt{e^{3 p+9}}$

Question 2

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

Accepted Answer

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

Question 3

Provide an appropriate response.
-The graph of an exponential function is given. Which of the following is the correct equation of the function?

Accepted Answer

A)  $y=0.45^{x}$ 
B)  $y=3.9^{x}$ 
C)  $\mathrm{y}=2.8^{\mathrm{x}}$ 
D)  $y=0.73^{x}$ 
A)  $y=0.45^{x}$ 
B)  $y=3.9^{x}$ 
C)  $\mathrm{y}=2.8^{\mathrm{x}}$ 
D)  $y=0.73^{x}$

Question 4

Write the expression as a sum and/or a difference of logarithms with all variables to the first degree.
-$\log 2 w(v+2)$

Accepted Answer

A)  $\log 2 w+\log 2 v+\log 4$ 
B)  $\log 2+\log w+\log (v+2)$ 
C)  $2 \log \mathrm{w}+\log (\mathrm{v}+2)$ 
D)  $\log 2+\log \mathrm{w}+\log \mathrm{v}+\log 2$ 
A)  $\log 2 w+\log 2 v+\log 4$ 
B)  $\log 2+\log w+\log (v+2)$ 
C)  $2 \log \mathrm{w}+\log (\mathrm{v}+2)$ 
D)  $\log 2+\log \mathrm{w}+\log \mathrm{v}+\log 2$

Question 5

Solve the problem.
-Use the formula $P=I e^{k t}$. A bacterial culture has an initial population of 10,000 . If its population declines to 3000 in 2 hours, what will it be at the end of 4 hours?

Accepted Answer

A)  450 
B)  900 
C)  4481 
D)  3500 
A)  450 
B)  900 
C)  4481 
D)  3500

Question 6

Find the value of the expression.
-$\ln 1$

Accepted Answer

A)  1 
B)  0 
C)  $\mathrm{e}$ 
D)  -1 
A)  1 
B)  0 
C)  $\mathrm{e}$ 
D)  -1

Question 7

Use a calculator to evaluate the logarithm.
-$\log 3.45$

Accepted Answer

A)  0.5250 
B)  0.5378 
C)  0.5502 
D)  1.2384 
A)  0.5250 
B)  0.5378 
C)  0.5502 
D)  1.2384

Question 8

Provide an appropriate response.
-The graph of an exponential function is given. Which of the following is the correct equation of the function?

Accepted Answer

A)  $y=0.74^{x}$ 
B)  $\mathrm{y}=1.9^{\mathrm{x}}$ 
C)  $y=3.6^{x}$ 
D)  $y=0.26^{x}$ 
A)  $y=0.74^{x}$ 
B)  $\mathrm{y}=1.9^{\mathrm{x}}$ 
C)  $y=3.6^{x}$ 
D)  $y=0.26^{x}$

Question 9

Solve the exponential equation.
-$7^{X}=7^{8}$

Accepted Answer

A)  56 
B)  8 
C)  -8 
D)  7 
A)  56 
B)  8 
C)  -8 
D)  7

Question 10

Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent positive numbers.
-$3 \ln (x+8)-6 \ln \left(x^{2}+7\right)$

Accepted Answer

A)  $\ln \left(\frac{3(x+8)}{\left(x^{2}+7\right)^{6}}\right)$ 
B)  $\ln \left(\frac{6(x+8)}{\left(x^{2}+7\right)^{3}}\right)$ 
C)  $\ln \left(\frac{(x+8)^{3}}{\left(x^{2}+7\right)^{6}}\right)$ 
D)  $\ln \left(\frac{(x+8)^{6}}{\left(x^{2}+7\right)^{3}}\right)$ 
A)  $\ln \left(\frac{3(x+8)}{\left(x^{2}+7\right)^{6}}\right)$ 
B)  $\ln \left(\frac{6(x+8)}{\left(x^{2}+7\right)^{3}}\right)$ 
C)  $\ln \left(\frac{(x+8)^{3}}{\left(x^{2}+7\right)^{6}}\right)$ 
D)  $\ln \left(\frac{(x+8)^{6}}{\left(x^{2}+7\right)^{3}}\right)$

Question 11

Write the logarithmic and exponential equations associated with the display.
-$g(x)=\ln x$

Accepted Answer

A)  $\ln 5.75=0.75966784469 ; \mathrm{e}^{0.75966784469}=5.75$ 
B)  $\ln 0.75966784469=5.75 ; \mathrm{e}^{5.75}=0.75966784469$ 
C)  $\ln 1.7491998548=5.75 ; \mathrm{e}^{5.75}=1.7491998548$ 
D)  $\ln 5.75=1.7491998548 ; \mathrm{e}^{1.7491998548}=5.75$ 
A)  $\ln 5.75=0.75966784469 ; \mathrm{e}^{0.75966784469}=5.75$ 
B)  $\ln 0.75966784469=5.75 ; \mathrm{e}^{5.75}=0.75966784469$ 
C)  $\ln 1.7491998548=5.75 ; \mathrm{e}^{5.75}=1.7491998548$ 
D)  $\ln 5.75=1.7491998548 ; \mathrm{e}^{1.7491998548}=5.75$

Question 12

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

Accepted Answer

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

Question 13

Solve the equation.
-$\log _{9}(x-8)+\log 9(x-8)=1$

Accepted Answer

A)  $-\sqrt{65}, \sqrt{65}$ 
B)  11 
C)  $\sqrt{65}$ 
D)  - 11,11 
A)  $-\sqrt{65}, \sqrt{65}$ 
B)  11 
C)  $\sqrt{65}$ 
D)  - 11,11

Question 14

Classify the function as a linear, quadratic, or exponential.
-$f(x)=x^{2}+8$

Accepted Answer

A)  Exponential 
B)  Quadratic 
C)  Linear 
A)  Exponential 
B)  Quadratic 
C)  Linear

Question 15

Solve the equation for $c$.
-$(6-\mathrm{m})=\log (7 \mathrm{c}+8)$

Accepted Answer

A)  $7\left(10^{6}-m-8\right)$ 
B)  $\frac{10^{6}-\mathrm{m}+8}{7}$ 
C)  $\frac{10^{6}-\mathrm{m}-8}{7}$ 
D)  $10^{6}-m-8$ 
A)  $7\left(10^{6}-m-8\right)$ 
B)  $\frac{10^{6}-\mathrm{m}+8}{7}$ 
C)  $\frac{10^{6}-\mathrm{m}-8}{7}$ 
D)  $10^{6}-m-8$

Question 16

Solve the equation.
-$\log _{25} x=\frac{1}{2}$

Accepted Answer

A)  5 
B)  0.00000003 
C)  $33,554,432$ 
D)  625 
A)  5 
B)  0.00000003 
C)  $33,554,432$ 
D)  625

Question 17

Express the following in terms of $u$ and $v$, where $u=\ln x$ and $v=\ln y$. For example, $\ln x=3(\ln x)=3 u$.
-$\ln \left(\frac{\sqrt{x}}{y^{4}}\right)$

Accepted Answer

A)  $4 \ln \mathrm{v}-\frac{\ln \mathrm{u}}{2}$ 
B)  $4 \mathrm{v}-\mathrm{u}$ 
C)  $\frac{u}{2}+4 v$ 
D)  $\frac{u}{2}-4 v$ 
A)  $4 \ln \mathrm{v}-\frac{\ln \mathrm{u}}{2}$ 
B)  $4 \mathrm{v}-\mathrm{u}$ 
C)  $\frac{u}{2}+4 v$ 
D)  $\frac{u}{2}-4 v$

Question 18

Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent positive numbers.
-$\log 8+\log 16-\log 2$

Accepted Answer

A)  $\log 4$ 
B)  $\log 3$ 
C)  $\log 64$ 
D)  $\log 15$ 
A)  $\log 4$ 
B)  $\log 3$ 
C)  $\log 64$ 
D)  $\log 15$

Question 19

Solve.
-In a town whose population is 3500 , a disease creates an epidemic. The number $\mathrm{N}$ of people infected $t$ days after the disease has begun is given by the function
$\mathrm{N}(\mathrm{t})=\frac{3500}{1+18 \cdot \mathrm{e}^{-0.8 \mathrm{t}}}$
Find the number infected after 16 days.

Accepted Answer

A)  3502 
B)  3498 
C)  3500 
D)  3503 
A)  3502 
B)  3498 
C)  3500 
D)  3503

Question 20

Express the following in terms of $u$ and $v$, where $u=\ln x$ and $v=\ln y$. For example, $\ln x=3(\ln x)=3 u$.
-$\ln \left(3 x^{2} y^{3}\right)$

Accepted Answer

A)  $\ln 5+3 u-2 v$ 
B)  $\ln 3+2 u-3 v$ 
C)  $3 u+2 v+\ln 5$ 
D)  $\ln 3+2 u+3 v$ 
A)  $\ln 5+3 u-2 v$ 
B)  $\ln 3+2 u-3 v$ 
C)  $3 u+2 v+\ln 5$ 
D)  $\ln 3+2 u+3 v$

Solve the equation for $c$ . - $(3 \mathrm{p}+9)=\ln (2 \mathrm{c})+\ln \mathrm{c}$

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

Provide an appropriate response. -The graph of an exponential function is given. Which of the following is the correct equation of the function?

Write the expression as a sum and/or a difference of logarithms with all variables to the first degree. - $\log 2 w(v+2)$

Solve the problem. -Use the formula $P=I e^{k t}$ . A bacterial culture has an initial population of 10,000 . If its population declines to 3000 in 2 hours, what will it be at the end of 4 hours?

Find the value of the expression. - $\ln 1$

Use a calculator to evaluate the logarithm. - $\log 3.45$

Provide an appropriate response. -The graph of an exponential function is given. Which of the following is the correct equation of the function?

Solve the exponential equation. - $7^{X}=7^{8}$

Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent positive numbers. - $3 \ln (x+8)-6 \ln \left(x^{2}+7\right)$

Write the logarithmic and exponential equations associated with the display. - $g(x)=\ln x$ $Write the logarithmic and exponential equations associated with the display. - g(x)=\ln x$

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

Solve the equation. - $\log _{9}(x-8)+\log 9(x-8)=1$

Classify the function as a linear, quadratic, or exponential. - $f(x)=x^{2}+8$

Solve the equation for $c$ . - $(6-\mathrm{m})=\log (7 \mathrm{c}+8)$

Solve the equation. - $\log _{25} x=\frac{1}{2}$

Express the following in terms of $u$ and $v$ , where $u=\ln x$ and $v=\ln y$ . For example, $\ln x=3(\ln x)=3 u$ . - $\ln \left(\frac{\sqrt{x}}{y^{4}}\right)$

Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent positive numbers. - $\log 8+\log 16-\log 2$

Solve. -In a town whose population is 3500 , a disease creates an epidemic. The number $\mathrm{N}$ of people infected $t$ days after the disease has begun is given by the function $\mathrm{N}(\mathrm{t})=\frac{3500}{1+18 \cdot \mathrm{e}^{-0.8 \mathrm{t}}}$ Find the number infected after 16 days.

Express the following in terms of $u$ and $v$ , where $u=\ln x$ and $v=\ln y$ . For example, $\ln x=3(\ln x)=3 u$ . - $\ln \left(3 x^{2} y^{3}\right)$

Algebra and Equations

Graphs, Lines, and Inequalities

Functions and Graphs

Mathematics of Finance

Systems of Linear Equations and Matrices

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Sets and Probability

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Introduction to Statistics

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Exam 4: Exponential and Logarithmic Functions

Solve the equation for ccc . - (3p+9)=ln⁡(2c)+ln⁡c(3 \mathrm{p}+9)=\ln (2 \mathrm{c})+\ln \mathrm{c}(3p+9)=ln(2c)+lnc

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

Provide an appropriate response. -The graph of an exponential function is given. Which of the following is the correct equation of the function?

Write the expression as a sum and/or a difference of logarithms with all variables to the first degree. - log⁡2w(v+2)\log 2 w(v+2)log2w(v+2)

Solve the problem. -Use the formula P=IektP=I e^{k t}P=Iekt . A bacterial culture has an initial population of 10,000 . If its population declines to 3000 in 2 hours, what will it be at the end of 4 hours?

Find the value of the expression. - ln⁡1\ln 1ln1

Use a calculator to evaluate the logarithm. - log⁡3.45\log 3.45log3.45

Provide an appropriate response. -The graph of an exponential function is given. Which of the following is the correct equation of the function?

Solve the exponential equation. - 7X=787^{X}=7^{8}7X=78

Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent positive numbers. - 3ln⁡(x+8)−6ln⁡(x2+7)3 \ln (x+8)-6 \ln \left(x^{2}+7\right)3ln(x+8)−6ln(x2+7)

Write the logarithmic and exponential equations associated with the display. - g(x)=ln⁡xg(x)=\ln xg(x)=lnx

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

Solve the equation. - log⁡9(x−8)+log⁡9(x−8)=1\log _{9}(x-8)+\log 9(x-8)=1log9​(x−8)+log9(x−8)=1

Classify the function as a linear, quadratic, or exponential. - f(x)=x2+8f(x)=x^{2}+8f(x)=x2+8

Solve the equation for ccc . - (6−m)=log⁡(7c+8)(6-\mathrm{m})=\log (7 \mathrm{c}+8)(6−m)=log(7c+8)

Solve the equation. - log⁡25x=12\log _{25} x=\frac{1}{2}log25​x=21​

Express the following in terms of uuu and vvv , where u=ln⁡xu=\ln xu=lnx and v=ln⁡yv=\ln yv=lny . For example, ln⁡x=3(ln⁡x)=3u\ln x=3(\ln x)=3 ulnx=3(lnx)=3u . - ln⁡(xy4)\ln \left(\frac{\sqrt{x}}{y^{4}}\right)ln(y4x​​)

Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent positive numbers. - log⁡8+log⁡16−log⁡2\log 8+\log 16-\log 2log8+log16−log2

Express the following in terms of uuu and vvv , where u=ln⁡xu=\ln xu=lnx and v=ln⁡yv=\ln yv=lny . For example, ln⁡x=3(ln⁡x)=3u\ln x=3(\ln x)=3 ulnx=3(lnx)=3u . - ln⁡(3x2y3)\ln \left(3 x^{2} y^{3}\right)ln(3x2y3)

Algebra and Equations

Graphs, Lines, and Inequalities

Functions and Graphs

Mathematics of Finance

Systems of Linear Equations and Matrices

Linear Programming

Sets and Probability

Counting, Probability Distributions, and Further Topics in Probability

Introduction to Statistics

Differential Calculus

Applications of the Derivative

Integral Calculus

Multivariate Calculus

Filters

Solve the equation for $c$ . - $(3 \mathrm{p}+9)=\ln (2 \mathrm{c})+\ln \mathrm{c}$

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

Write the expression as a sum and/or a difference of logarithms with all variables to the first degree. - $\log 2 w(v+2)$

Solve the problem. -Use the formula $P=I e^{k t}$ . A bacterial culture has an initial population of 10,000 . If its population declines to 3000 in 2 hours, what will it be at the end of 4 hours?

Find the value of the expression. - $\ln 1$

Use a calculator to evaluate the logarithm. - $\log 3.45$

Solve the exponential equation. - $7^{X}=7^{8}$

Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent positive numbers. - $3 \ln (x+8)-6 \ln \left(x^{2}+7\right)$

Write the logarithmic and exponential equations associated with the display. - $g(x)=\ln x$ $Write the logarithmic and exponential equations associated with the display. - g(x)=\ln x$

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

Solve the equation. - $\log _{9}(x-8)+\log 9(x-8)=1$

Classify the function as a linear, quadratic, or exponential. - $f(x)=x^{2}+8$

Solve the equation for $c$ . - $(6-\mathrm{m})=\log (7 \mathrm{c}+8)$

Solve the equation. - $\log _{25} x=\frac{1}{2}$

Express the following in terms of $u$ and $v$ , where $u=\ln x$ and $v=\ln y$ . For example, $\ln x=3(\ln x)=3 u$ . - $\ln \left(\frac{\sqrt{x}}{y^{4}}\right)$

Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent positive numbers. - $\log 8+\log 16-\log 2$

Express the following in terms of $u$ and $v$ , where $u=\ln x$ and $v=\ln y$ . For example, $\ln x=3(\ln x)=3 u$ . - $\ln \left(3 x^{2} y^{3}\right)$