Question 1

Which of the following correctly applies the product rule for exponents to simplify $$x^3$$ \cdot $$x^5$$?

Accepted Answer

$$x^{8}$$

Question 2

Simplify the expression $$\dfrac{6x^7$ n^5$}{3x^2$ n^6$}.$$

Accepted Answer

$$2x^5$$ $$n^{-1}$$

Question 3

Which of the following is NOT a correct property of exponents?

Accepted Answer

$$a^m + a^n = a$$^{m+n}$$

Question 4

Write the exponential equation $$5^x = 90 in $$logarithmic form.

Accepted Answer

$$\log_5$ 90 = x$$

Question 5

Evaluate $$\log_{2}(\dfrac{1}{8})$$ without a calculator.

Accepted Answer

$$-3$$

Question 6

Which of the following is equivalent to $$\sqrt[3]{x^5$}$$ written with rational exponents?

Accepted Answer

$$x^{5/3}$$

Question 7

If $$\log_{b}(x) = 2$$, what is $$x in $$terms of $$b$$?

Accepted Answer

$$x = b^2$

Question 8

Condense the expression $$\log_5$(x+4) + \log_5$(2x+1)$$ using properties of logarithms.

Accepted Answer

$$\log_5$((x+4)(2x+1))$$

Question 9

Solve for $$x$$: $$2^{x+2} = 100$.

Accepted Answer

$$x = \log_2$ 25$$

Question 10

Which of the following is the correct change of base formula for $$\log_3$ 38$$?

Accepted Answer

$$\dfrac{\ln 38}{\ln 3}$$

Question 11

A population triples every time period. If the initial population is 5,600, which equation models the population $$y$$ after $$x$$ time periods?

Accepted Answer

$$y = 5600 \cdot 3^x$$

Question 12

Which of the following is a common error involving exponents?

Accepted Answer

$$(a+b)^n = a^n + b^n$$

Question 13

If $$\log_{10}(x) = 3$$, what is the value of $$x$$?

Accepted Answer

$$x = 1000$$

Question 14

Simplify $$e^{\ln(7)}.$$

Accepted Answer

$$7$$

Question 15

A medication's concentration in the bloodstream decreases according to $$y = 50 - 30 \log_2$(x)$$, where $$x is $$the number of days after administration. After how many days will the concentration be 35 units? (Round to one decimal place.)

Accepted Answer

$$x = 2$$^{1/3}$$ \approx 1.3$$ days

Question 16

Which of the following is the correct way to write $$\log_{a}(M) + \log_{a}(N) as a $$single logarithm?

Accepted Answer

$$\log_{a}(MN)$$

Question 17

If $$\ln(x) = 2$$, what is the value of $$x$$?

Accepted Answer

$$x = e^2$

Question 18

Which of the following is the correct exponential form of the logarithmic equation $$\log_4$(x-2) = 3$$?

Accepted Answer

$$x-2 = 4^3$

Question 19

A bank account grows according to $$y = 45,000 \cdot 1.06^x$$, where $$x is $$the number of years. What is the growth factor per year?

Accepted Answer

$$1.06$$

College Algebra Chapter 2 Study Notes: Exponents, Logarithms, and Exponential Growth

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