Question 1

Evaluate $$e^{1/6} to $$six decimal places. Which of the following is correct?

Accepted Answer

$$e^{1/6}$$ \approx 1.181360$$

Question 2

Which of the following is the correct table of values for the function $$f(x) = 5^x$$?

Accepted Answer

For $$x = -2, -1, 0, 1, 2$$, $$y = \frac{1}{25}, \frac{1}{5}, 1, 5, 25$$

Question 3

Given $$y = 2^x$$, which of the following points lies on the graph of $$f(x) = 2^x + 1$$?

Accepted Answer

$$(0, 2)$$

Question 4

Solve the exponential equation $$3^{2x} = 9^x$ for x$.

Accepted Answer

$$x = 1$$

Question 5

A bank offers a 6\% annual interest rate compounded monthly. If you invest $$\17$$,000$$ for 12 years, what is the value of your investment? Use A = P$$ \left(1 + \frac{r}{n}\$$right)^{nt}$ and round to the nearest cent.

Accepted Answer

$$A = \34$$,862.76$

Question 6

Rewrite the logarithmic equation $$\log W = Z as an $$exponential equation.

Accepted Answer

$$W = 10^Z$$

Question 7

Evaluate $$\ln e^8$ + \ln e^3$ without a calculator.

Accepted Answer

$$11$$

Question 8

Find the domain of the logarithmic function $$f(x) = \log_6$(x^2 - 3x - 54$$)$. Which interval is correct?

Accepted Answer

$$(-\infty, -6) \cup (9, \infty)$$

Question 9

Expand $$\ln \left(\frac{e^9$}{r}\right)$$ using properties of logarithms.

Accepted Answer

$$9 - \ln r$$

Question 10

Use properties of logarithms to evaluate $$\log_6$ 11 - \log_6$ 8.$$

Accepted Answer

$$\log_6$ \left(\frac{11}{8}\right)$$

Question 11

Rewrite $$\log_4$(x-9) + \log_4$(x+9) as a $$single logarithm.

Accepted Answer

$$\log_4$(x^2 - 81$$)$

Question 12

Solve for $$x$$: $$\log_3$ x = \log_6$ 3.$$

Accepted Answer

$$x = 36$$

Question 13

Use the change of base formula to approximate $$\log_5$ 100 to $$four decimal places.

Accepted Answer

$$5.7227$$

Question 14

Solve $$e^x = 4$$ for $$x$$ and give the exact solution using a natural logarithm.

Accepted Answer

$$x = \ln 4$$

Question 15

Solve the logarithmic equation $$\log_4$(5x + 3) - \log_4$(x - 3) = 2$$ for $$x.$$

Accepted Answer

$$x = \frac{51}{11}$$

Question 16

A $$\113$$,000$$ investment earns 7.5\% annual interest compounded monthly for 20 years. What is the final amount? Use A = P$$ \left(1 + \frac{r}{n}\$$right)^{nt}$ and round to the nearest cent.

Accepted Answer

$$A = \504$$,072.32$

Question 17

Which property of logarithms allows you to write $$\ln e^8$ + \ln e^3$ = \ln (e^8$ \cdot e^3$)$$?

Accepted Answer

Product property

Question 18

If $$f(x) = \log_6$(x^2 - 3x - 54$$)$$, for which value is f(x$$)$ undefined?

Accepted Answer

$$x = -6$$

Question 19

Which of the following is the correct application of the quotient rule for logarithms?

Accepted Answer

$$\log_b \left(\frac{M}{N}\right) = \log_b M - \log_b N$$

Question 20

Which of the following is the correct change of base formula for $$\log_5$ 100$$?

Accepted Answer

$$\log_5$ 100 = \frac{\ln 100}{\ln 5}$$

College Algebra Chapter 5 Review: Exponential and Logarithmic Functions

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