Question 1

Which of the following correctly expands $$\log_2$\left(\frac{8}{x}\right)$$ using logarithmic properties?

Accepted Answer

$$\log_2$(8) - \log_2$(x)$$

Question 2

Simplify $$\log_{0.1}(10x^2$)$$ using logarithmic properties.

Accepted Answer

$$2\log_{0.1}(x) - 1$$

Question 3

Expand $$\ln\left(\frac{3}{ex}\$$right)^2$$ using logarithmic properties.

Accepted Answer

$$2\ln(3) - 2\ln(e) - 2\ln(x)$$

Question 4

Which of the following is the correct expansion for $$\log\left(\sqrt[3]{\frac{100x^2$}{yz^5$}}\right)$$?

Accepted Answer

$$\frac{1}{3}\log(100) + \frac{2}{3}\log(x) - \frac{1}{3}\log(y) - \frac{5}{3}\log(z)$$

Question 5

Rewrite $$\log_{117}(x^2$ - 4)$$ using logarithmic properties.

Accepted Answer

$$\log_{117}(x + 2) + \log_{117}(x - 2)$$

Question 6

Combine $$\log(x) + 2\log(y) - \log(z)$$ into a single logarithm.

Accepted Answer

$$\log\left(\frac{xy^2$}{z}\right)$$

Question 7

Express $$4\log_2$(x) + 3 as a $$single logarithm.

Accepted Answer

$$\log_2$(8x^4$$)$

Question 8

Simplify $$-\ln(x) - \frac{1}{2}$$ using logarithmic properties.

Accepted Answer

$$\ln\left(\frac{1}{x\sqrt{e}}\right)$$

Question 9

Which property of exponential functions explains why $$y = 2^x is $$always increasing?

Accepted Answer

The base $$b \u003e 1$$ causes the function to be strictly increasing for all $$x$$

Question 10

What is the domain and range of the exponential function $$f(x) = b^x$$ for $$b \u003e 0$$, $$b 
eq 1$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(0, \infty)$$

Question 11

Which of the following statements about logarithmic functions is correct?

Accepted Answer

The domain of $$f(x) = \log_b(x) is$$ $$(0, \infty)$$ and the range is $$(-\infty, \infty)$$

Question 12

If $$f(x) = 2^x$$ and $$g(x) = 2$$^{-x}$$, how are their graphs related?

Accepted Answer

The graph of $$g(x) is a $$reflection of $$f(x)$$ across the y-axis

Question 13

Which of the following is true about the inverse of an exponential function $$f(x) = b^x$$?

Accepted Answer

The inverse is $$f^{-1}(x$$) = \log_b(x)$$

Question 14

Which property of logarithms allows you to rewrite $$\log_b(MN) as$$ $$\log_b(M) + \log_b(N)$$?

Accepted Answer

Product Rule

Question 15

Evaluate $$\log_9$(9^7$$)$ without a calculator.

Accepted Answer

7

Question 16

Which of the following is NOT a property of exponential functions $$f(x) = b^x$$ for $$b \u003e 1$$?

Accepted Answer

The function is always decreasing

Question 17

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, are f$ and g$ inverses of each other on $$(-\infty, \infty)$$?

Accepted Answer

No, because $$f(x) is $$not one-to-one on $$(-\infty, \infty)$$

Question 18

Which logarithmic property allows you to rewrite $$\log_b(M^k) as$$ $$k\log_b(M)$$?

Accepted Answer

Power Rule

1.3 Inverse, Exponential, and Logarithmic Functions

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