Question 1

Provide an appropriate response.
-When solving an exponential equation using logarithms, when is it easier to use common logarithms?

Accepted Answer

When the b

Question 2

Match the equation to the graph.
-

Accepted Answer

A)  $y=\ln x$ 
B)  $y=\log x$ 
C)  $y=e^{x}$ 
D)  $y=10^{x}$ 
A)  $y=\ln x$ 
B)  $y=\log x$ 
C)  $y=e^{x}$ 
D)  $y=10^{x}$

Question 3

Classify the function as a linear, quadratic, or exponential.
-$f(x)=2^{x-7}$

Accepted Answer

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

Question 4

Use a calculator to evaluate the logarithm.
-$\log 0.00457$

Accepted Answer

A)  -5.3882 
B)  -2.3497 
C)  -2.3307 
D)  -2.3401 
A)  -5.3882 
B)  -2.3497 
C)  -2.3307 
D)  -2.3401

Question 5

Write in logarithmic form.
-$\mathrm{e}^{-2}=0.1353$

Accepted Answer

A)  $-2=\log _{e} 0.1353$ 
B)  $0.1353=\log _{e}-2$ 
C)  $0.1353=\log _{-2} \mathrm{e}$ 
D)  $e=\log _{-2} 0.1353$ 
A)  $-2=\log _{e} 0.1353$ 
B)  $0.1353=\log _{e}-2$ 
C)  $0.1353=\log _{-2} \mathrm{e}$ 
D)  $e=\log _{-2} 0.1353$

Question 6

Solve the problem.
-The amount of particulate matter left in solution during a filtering process is given by the equation $P(x)=200(2)^{-0.8 n}$, where $n$ is the number of filtering steps. Find the amounts left for $\mathrm{n}=0$ and $\mathrm{n}=5$. (Round to the nearest whole number.)

Accepted Answer

A)  200,13 
B)  400,13 
C)  200,6 
D)  200,3200 
A)  200,13 
B)  400,13 
C)  200,6 
D)  200,3200

Question 7

Solve the problem.
-A certain radioactive isotope has a half-life of approximately 1900 years. How many years to the nearest year would be required for a given amount of this isotope to decay to $55 \%$ of that amount?

Accepted Answer

A)  1584 years 
B)  1639 years 
C)  855 years 
D)  2189 years 
A)  1584 years 
B)  1639 years 
C)  855 years 
D)  2189 years

Question 8

Express the following in terms of $u$ and $v$, where $u=\ln x$ and $v=\ln y$. For example, $\ln x=3(\ln x)=3 u$.
-$\ln \left(x^{7} \sqrt{y}\right)$

Accepted Answer

A)  $7 u+v$ 
B)  $7 \ln u+\frac{\ln v}{2}$ 
C)  $7 v+\frac{u}{2}$ 
D)  $7 u+\frac{v}{2}$ 
A)  $7 u+v$ 
B)  $7 \ln u+\frac{\ln v}{2}$ 
C)  $7 v+\frac{u}{2}$ 
D)  $7 u+\frac{v}{2}$

Question 9

Solve the problem.
-If an earthquake measured 5.9 on the Richter scale, what was the intensity of the earthquake? Use the formula M = log (A/Ao).

Accepted Answer

A)  365 
B)  79,433 
C)  630,957 
D)  794,328 
A)  365 
B)  79,433 
C)  630,957 
D)  794,328

Question 10

Use a calculator to evaluate the logarithm.
-$\log 280$

Accepted Answer

A)  2.4456 
B)  2.4487 
C)  5.6348 
D)  2.4472 
A)  2.4456 
B)  2.4487 
C)  5.6348 
D)  2.4472

Question 11

Use a calculator to evaluate the logarithm.
-$\log 0.0795$

Accepted Answer

A)  -2.5320 
B)  -1.0942 
C)  -1.0996 
D)  -1.1051 
A)  -2.5320 
B)  -1.0942 
C)  -1.0996 
D)  -1.1051

Question 12

Classify the function as a linear, quadratic, or exponential.
-f $(x)=-4 x-2$

Accepted Answer

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

Question 13

Solve the equation for $c$.
-$\log (8 \mathrm{c}-4)=\log (7-\mathrm{r})$

Accepted Answer

A)  $\frac{3-r}{8}$ 
B)  $\frac{11+r}{8}$ 
C)  $\frac{11-r}{8}$ 
D)  $\frac{7-r}{8}$ 
A)  $\frac{3-r}{8}$ 
B)  $\frac{11+r}{8}$ 
C)  $\frac{11-r}{8}$ 
D)  $\frac{7-r}{8}$

Question 14

Solve the problem.
-The half-life of an element is $4.2 \times 10^{9} \mathrm{yr}$. How long does it take a sample of the element to decay to $\frac{2}{5}$ of its original mass? Use $\mathrm{A}=\mathrm{A}_{0} \frac{1}{2}^{(\mathrm{t} / \mathrm{T})}$ where $\mathrm{A}_{0}$ is the initial amount, $\mathrm{T}$ is the half-life, and $\mathrm{t}$ is the time. (Express results in scientific notation, rounded to the nearest hundredth.)

Accepted Answer

A)  $9.37 \times 10^{8} \mathrm{yr}$ 
B)  $2.67 \times 10^{9} \mathrm{yr}$ 
C)  $3.94 \times 10^{9} \mathrm{yr}$ 
D)  $5.55 \times 10^{9} \mathrm{yr}$ 
A)  $9.37 \times 10^{8} \mathrm{yr}$ 
B)  $2.67 \times 10^{9} \mathrm{yr}$ 
C)  $3.94 \times 10^{9} \mathrm{yr}$ 
D)  $5.55 \times 10^{9} \mathrm{yr}$

Question 15

Provide an appropriate response.
-Why is evaluating ln ea much like answering the question "What is the name of the boy whose name is Jose?

Accepted Answer

The reason why evaluating ln e^a is much l

Question 16

Convert to exponential form.
-$\log _{5} \frac{1}{125}=-3$

Accepted Answer

A)  $5^{125}=3$ 
B)  $\left(\frac{1}{125}\right)^{3}=5$ 
C)  $3^{5}=\frac{1}{125}$ 
D)  $5^{-3}=\frac{1}{125}$ 
A)  $5^{125}=3$ 
B)  $\left(\frac{1}{125}\right)^{3}=5$ 
C)  $3^{5}=\frac{1}{125}$ 
D)  $5^{-3}=\frac{1}{125}$

Question 17

Solve the equation.
-$4^{\mathrm{X}}=20$

Accepted Answer

A)  2.161 
B)  5.000 
C)  0.463 
D)  1.609 
A)  2.161 
B)  5.000 
C)  0.463 
D)  1.609

Question 18

Find the value of the expression.
-$\log _{10} 10$

Accepted Answer

A)  -1 
B)  1 
C)  0 
D)  10 
A)  -1 
B)  1 
C)  0 
D)  10

Question 19

Provide an appropriate response.
-What is the difference between ln a and log a?

Accepted Answer

The difference between ln a and log a li

Question 20

Solve the problem.
-The number of species in a sample is given by $S(n)=0.88 \ln \left(1+\frac{n}{0.88}\right)$, where $n$ is the number of individuals in the sample and the constant 0.88 indicates the diversity of species in the community. Find $\mathrm{S}(\mathrm{n})$ when $\mathrm{n}=874$. Round to the nearest unit.

Accepted Answer

A)  8 
B)  0 
C)  6 
D)  3 
A)  8 
B)  0 
C)  6 
D)  3

Provide an appropriate response. -When solving an exponential equation using logarithms, when is it easier to use common logarithms?

Match the equation to the graph. -

Classify the function as a linear, quadratic, or exponential. - $f(x)=2^{x-7}$

Use a calculator to evaluate the logarithm. - $\log 0.00457$

Write in logarithmic form. - $\mathrm{e}^{-2}=0.1353$

Solve the problem. -The amount of particulate matter left in solution during a filtering process is given by the equation $P(x)=200(2)^{-0.8 n}$ , where $n$ is the number of filtering steps. Find the amounts left for $\mathrm{n}=0$ and $\mathrm{n}=5$ . (Round to the nearest whole number.)

Solve the problem. -A certain radioactive isotope has a half-life of approximately 1900 years. How many years to the nearest year would be required for a given amount of this isotope to decay to $55 \%$ of that amount?

Express the following in terms of $u$ and $v$ , where $u=\ln x$ and $v=\ln y$ . For example, $\ln x=3(\ln x)=3 u$ . - $\ln \left(x^{7} \sqrt{y}\right)$

Solve the problem. -If an earthquake measured 5.9 on the Richter scale, what was the intensity of the earthquake? Use the formula M = log (A/Ao).

Use a calculator to evaluate the logarithm. - $\log 280$

Use a calculator to evaluate the logarithm. - $\log 0.0795$

Classify the function as a linear, quadratic, or exponential. -f $(x)=-4 x-2$

Solve the equation for $c$ . - $\log (8 \mathrm{c}-4)=\log (7-\mathrm{r})$

Provide an appropriate response. -Why is evaluating ln e^a much like answering the question "What is the name of the boy whose name is Jose?

Convert to exponential form. - $\log _{5} \frac{1}{125}=-3$

Solve the equation. - $4^{\mathrm{X}}=20$

Find the value of the expression. - $\log _{10} 10$

Provide an appropriate response. -What is the difference between ln a and log a?

Algebra and Equations

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Systems of Linear Equations and Matrices

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Introduction to Statistics

Differential Calculus

Applications of the Derivative

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Exam 4: Exponential and Logarithmic Functions