Question 1

Solve the exponential equation algebraically. Approximate the result to three deci- mal places.

Accepted Answer

E

Question 2

Write the exponential equation in logarithmic form.

Accepted Answer

The exponential equation can be written as:
$$4^{-2}=\frac{1}{16}$$
Now, taking the logarithm of both sides with base 4:
$$\log_4(4^{-2})=\log_4(\frac{1}{16})$$
$$-2=\log_4(4^{-2})=\log_4(\frac{1}{16})$$
Hence, the correct choice is D.

Question 3

Evaluate the logarithm     using the change of base formula. Round to 3 decimal places.&#10;A) -1.745&#10;B) -0.692&#10;C) 0.630&#10;D) 0.273&#10;E) -0.573

Accepted Answer

E

Question 4

Evaluate the logarithm using the change-of-base formula. Round your result to three decimal places.

Accepted Answer

The change-of-base formula allows us to write $\log _ { 4 } 9$ as $\frac{\log 9}{\log 4}$ or $\frac{\ln 9}{\ln 4}$, where $\log$ is the logarithm base 10 and $\ln$ is the natural logarithm (base $e$). Using a calculator, this evaluates to approximately 1.585.

Question 5

Use the One-to-One Property to solve the equation for x.

Accepted Answer

Using the One-to-One Property, we can set the expressions inside the logarithms equal to each other:

\begin{align*}
\log_2(8x+2)&=\log_2(14)\
8x+2&=14\
8x&=12\
x&=\frac{3}{2}
\end{align*}

Therefore, the answer is (C).

Question 6

Solve the exponential equation algebraically. Approximate the result to three deci- mal places.

Accepted Answer

The answer of Solve the exponential equation algebraically. Approximate the...

Question 7

Use a graphing utility to construct a table of values for the function. Round your answer to two decimal places.

Accepted Answer

After using a graphing utility to plot the function, we can see that the values in choice E match the shape of the graph. Furthermore, the function is clearly positive for all values of x in the domain, so choices A, B, and C can be eliminated. Additionally, the function is decreasing as x increases, so choice D can also be eliminated. Therefore, the best choice is E.

Question 8

Find the exact value of the logarithmic expression without using a calculator.

Accepted Answer

We can simplify the expression first:

$\log _ { 9 } \sqrt [ 3 ] { 9 } = \log _ { 9 } 9^{\frac13} = \frac13$

Therefore, the answer is (B).

Question 9

Evaluate the function at the indicated value of

Accepted Answer

If we substitute $a ^ { 2 }$ for x, we get $g(a^2)=\log_a(a^2)=2$. Therefore, the answer is choice D, 2.

Question 10

Evaluate the function at the indicated value of   . Round your result to three deci- mal places.

Accepted Answer

Plugging in 1.7 for x, we get $0.5^{1.7} \approx 0.308$ rounding to 3 decimal places. Therefore, the answer is choice C.

Question 11

Rewrite the logarithm as a ratio of common logarithms.

Accepted Answer

The answer of Rewrite the logarithm as a ratio of...

Question 12

Select the graph of the exponential function.

Accepted Answer

The answer of Select the graph of the exponential function....

Question 13

Determine the principal that must be invested at rate r, compounded monthly, so that   will be available for retirement in t years.   (Round the answer upto 2 decimal places.)

Accepted Answer

The answer of Determine the principal that must be invested...

Question 14

Write the exponential equation in logarithmic form.

Accepted Answer

The answer of Write the exponential equation in logarithmic form....

Question 15

Determine whether the given x-value is a solution (or an approximate solution) of the equation.  &#10;A) No&#10;B) Yes

Accepted Answer

The answer of Determine whether the given x-value is a...

Question 16

Condense the expression to the logarithm of a single quantity.

Accepted Answer

The answer of Condense the expression to the logarithm of...

Question 17

Evaluate the function at the indicated value of   . Round your result to three deci- mal places.

Accepted Answer

The answer of Evaluate the function at the indicated value...

Question 18

Solve the logarithmic equation algebraically. Approximate the result to three deci- mal places.

Accepted Answer

The answer of Solve the logarithmic equation algebraically. Approximate the...

Question 19

Write the logarithmic equation in exponential form.

Accepted Answer

The answer of Write the logarithmic equation in exponential form....

Question 20

Solve for   . Approximate the result to three decimal places.

Accepted Answer

The answer of Solve for   . Approximate the...

Question 21

Solve for   . Approximate the result to three decimal places.

Accepted Answer

The answer of Solve for   . Approximate the...

Question 22

Write the logarithmic equation in exponential form.

Accepted Answer

The answer of Write the logarithmic equation in exponential form....

Question 23

Select a scatter plot of the given data.

Accepted Answer

The answer of Select a scatter plot of the given...

Question 24

Evaluate the logarithm using the change of base formula. Round to 3 decimal places.&#10;A) -0.473&#10;B) 0.226&#10;C) -0.571&#10;D) 0.519&#10;E) -2.115

Accepted Answer

The answer of Evaluate the logarithm using the change of...

Question 25

Solve the exponential equation algebraically. Approximate the result to three deci- mal places.

Accepted Answer

The answer of Solve the exponential equation algebraically. Approximate the...

Question 26

Evaluate the function at the indicated value of

Accepted Answer

The answer of Evaluate the function at the indicated value...

Question 27

Use a graphing utility to construct a table of values for the function. Round your answer to two decimal places.

Accepted Answer

The answer of Use a graphing utility to construct a...

Question 28

Evaluate the function at the indicated value of   . Round your result to three deci- mal places.

Accepted Answer

The answer of Evaluate the function at the indicated value...

Question 29

Write the exponential equation in logarithmic form.

Accepted Answer

The answer of Write the exponential equation in logarithmic form....

Question 30

Evaluate the logarithm using the change-of-base formula. Round your result to three decimal places.

Accepted Answer

The answer of Evaluate the logarithm using the change-of-base formula....

Question 31

Condense the expression to the logarithm of a single quantity.

Accepted Answer

The answer of Condense the expression to the logarithm of...

Question 32

Find the exponential model that   fits the points shown in the table.

Accepted Answer

The answer of Find the exponential model that  ...

Question 33

Find the magnitude R of ea&#10;A) 7.42&#10;B) 6.42&#10;C) 8.42&#10;D) 10.42&#10;E) 9.42

Accepted Answer

The answer of Find the magnitude R of ea&#10;A) 7.42&#10;B)...

Question 34

Find the exact value of the logarithmic expression without using a calculator.

Accepted Answer

The answer of Find the exact value of the logarithmic...

Question 35

Rewrite the logarithm as a ratio of common logarithms.

Accepted Answer

The answer of Rewrite the logarithm as a ratio of...

Question 36

Write the exponential equation in logarithmic form.

Accepted Answer

The answer of Write the exponential equation in logarithmic form....

Question 37

Select the graph of the exponential function.

Accepted Answer

The answer of Select the graph of the exponential function....

Question 38

Evaluate the function at the indicated value of   . Round your result to three deci- mal places.

Accepted Answer

The answer of Evaluate the function at the indicated value...

Question 39

Use the One-to-One Property to solve the equation for x.

Accepted Answer

The answer of Use the One-to-One Property to solve the...

Question 40

Determine whether the given x-value is a solution (or an approximate solution) of the equation.  &#10;A) No&#10;B) Yes

Accepted Answer

The answer of Determine whether the given x-value is a...

Question 41

Find the exponential model that   fits the points shown in the table.

Accepted Answer

The answer of Find the exponential model that  ...

Question 42

Find the magnitude R of ea&#10;A) 8.36&#10;B) 9.36&#10;C) 10.36&#10;D) 7.36&#10;E) 6.36

Accepted Answer

The answer of Find the magnitude R of ea&#10;A) 8.36&#10;B)...

Question 43

Solve the logarithmic equation algebraically. Approximate the result to three deci- mal places.

Accepted Answer

The answer of Solve the logarithmic equation algebraically. Approximate the...

Question 44

Solve the exponential equation algebraically. Approximate the result to three deci- mal places.

Accepted Answer

The answer of Solve the exponential equation algebraically. Approximate the...

Question 45

Determine the principal that must be invested at rate r, compounded monthly, so that   will be available for retirement in t years.   (Round the answer upto 2 decimal places.)

Accepted Answer

The answer of Determine the principal that must be invested...

Question 46

Select a scatter plot of the given data.

Accepted Answer

The answer of Select a scatter plot of the given...

Deck 3: Exponential and Logarithmic Functions