Question 1

Which of the following correctly applies the product rule for exponents to simplify $$x^5$$ 	imes $$x^7$$?

Accepted Answer

$$x^{5+7}$$ = $$x^{12}$$

Question 2

Simplify the expression $$\dfrac{25a$$^{10}$$}{b^2$}$$ using exponent rules.

Accepted Answer

$$25a^{10}b$$^{-2}$

Question 3

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

Accepted Answer

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

Question 4

Write the exponential equation $$3^p = 9 in $$logarithmic form.

Accepted Answer

$$\log_3$ 9 = p$$

Question 5

If $$\log_{10}(x) = 2$$, what is $$x in $$exponential form?

Accepted Answer

$$x = 10^2$

Question 6

Which of the following is the correct change of base formula for $$\log_5$ 38$$?

Accepted Answer

$$\dfrac{\ln 38}{\ln 5}$$

Question 7

Given the exponential growth function $$y = 5600 \cdot 3^x$$, what is the population after 4 time periods?

Accepted Answer

$$y = 5600 \cdot 81$$

Question 8

Simplify $$\sqrt{x^5$}$$ and write your answer with only positive exponents.

Accepted Answer

$$x^{5/2}$$

Question 9

Which of the following is the correct logarithmic regression equation for the sleep data: $$y = 17.3 - 3.3 \ln(x)$$?

Accepted Answer

$$y = 17.3 - 3.3 \ln(x)$$

Question 10

Condense the expression $$\log_5$(x+4) + \log_5$(3x+1)$$ using logarithm properties.

Accepted Answer

$$\log_5$((x+4)(3x+1))$$

Question 11

Solve for $$x$$: $$10^x = 2$$

Accepted Answer

$$x = \log_{10} 2$$

Question 12

If $$\log_2$(x) = 3$$, what is the value of $$x$$?

Accepted Answer

$$x = 8$$

Question 13

Which of the following is a common error involving exponents?

Accepted Answer

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

Question 14

Simplify $$e^{\ln(2)}$$ without a calculator.

Accepted Answer

$$2$$

Question 15

If $$\log_{10}(x) = 0$$, what is $$x$$?

Accepted Answer

$$x = 1$$

Question 16

Which of the following is the correct exponential growth equation for an initial population of 53 million that increases 3.4% every year?

Accepted Answer

$$y = 53 \cdot 1.034^x$$

Question 17

Condense $$\ln(x) + \ln(y) - \ln(z)$$ using logarithm properties.

Accepted Answer

$$\ln(xy/z)$$

Question 18

If $$x = 3$$, what is the value of $$y in $$the regression equation $$y = 17.3 - 3.3 \ln(x)$$?

Accepted Answer

$$y = 17.3 - 3.3 \ln(3)$$

Question 19

Which of the following is the correct way to write $$\log_3$(32)$$ using the change of base formula?

Accepted Answer

$$\dfrac{\ln 32}{\ln 3}$$

Question 20

Solve for $$x$$: $$7^x = 21$$

Accepted Answer

$$x = \dfrac{\log_{10} 21}{\log_{10} 7}$$

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

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