Question 1

Which of the following is the correct exponential form of the logarithmic equation $$3 = \log_7$ x$$?

Accepted Answer

$$x = 7^3$

Question 2

Rewrite the exponential equation $$e^y = 33 in $$logarithmic form.

Accepted Answer

$$y = \ln 33$$

Question 3

Evaluate $$\log_{10} 100.$$

Accepted Answer

$$2$$

Question 4

What is the value of $$\log_5$ \frac{1}{125}$$?

Accepted Answer

$$-3$$

Question 5

Which property of logarithms justifies that $$\log_b 1 = 0$$ for any base $$b \u003e 0$$, $$b 
eq 1$$?

Accepted Answer

Because $$b^0 = 1$

Question 6

If $$f(x) = \log_4$ (x - 5)$$, what is the domain of $$f(x)$$?

Accepted Answer

$$(5, \infty)$$

Question 7

Which of the following statements is TRUE about the graph of $$f(x) = \log_b x$$ for $$b \u003e 1$$?

Accepted Answer

It passes through the point $$(1, 0).$$

Question 8

Evaluate $$\log_3$ \sqrt[3]{3}.$$

Accepted Answer

$$1/3$$

Question 9

Which of the following is the correct logarithmic form of the exponential equation $$2^5 = x$?

Accepted Answer

$$5 = \log_2$ x$$

Question 10

Given $$f(x) = 29 + 48.8 \log(x + 1)$$ models the percentage of adult height attained by a boy of age $$x ($$from 5 to 15), what percentage has a boy attained at age 10?

Accepted Answer

$$29 + 48.8 \log(11)$$

Question 11

Which of the following is NOT a property of logarithms?

Accepted Answer

$$\log_b x = b^x$$

Question 12

What is the vertical asymptote of the graph $$f(x) = \log_4$ (x - 5)$$?

Accepted Answer

$$x = 5$$

Question 13

Which of the following is the correct evaluation of $$\log_{36} 6$$?

Accepted Answer

$$1/2$$

Question 14

If $$f(x) = \log_b x$$, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 15

Which of the following is the correct evaluation of $$\log_8$ 1$$?

Accepted Answer

$$0$$

Question 16

Which function is the inverse of $$f(x) = 3^x$$?

Accepted Answer

$$f^{-1}(x$$) = \$$log_3 x$

Question 17

If $$f(x) = \log_{1/2} x$$, which statement about its graph is TRUE?

Accepted Answer

It passes through $$(1, 0).$$

Question 18

Evaluate $$\ln e^5$.

Accepted Answer

$$5$$

Question 19

The function $$f(x) = 13.4 \ln x - 11.6$$ models the temperature increase in a car after $$x$$ minutes. What is the temperature increase after 30 minutes, to the nearest degree?

Accepted Answer

$$13.4 \ln 30 - 11.6$$

Question 20

Which of the following is the correct evaluation of $$\log_7$ 7^8$?

Accepted Answer

$$8$$

Study Notes: Logarithmic Functions (Precalculus, Section 3.2)

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