Question 1

Which of the following is the correct exponential form of the logarithmic equation $$y = \log_3$ 81$$?

Accepted Answer

$$3^y = 81$$

Question 2

Rewrite the exponential equation $$2^5 = 32$ in logarithmic form.

Accepted Answer

$$\log_2$ 32 = 5$$

Question 3

Evaluate $$\log_{10} 0.01.$$

Accepted Answer

$$-2$$

Question 4

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

Accepted Answer

Because $$b^1 = b$

Question 5

What is the domain of the function $$f(x) = \log_4$ (x - 2)$$?

Accepted Answer

$$(2, \infty)$$

Question 6

If $$f(x) = \log_2$ x$$ and $$g(x) = 2^x$$, which statement is true about their graphs?

Accepted Answer

They are reflections of each other across the line $$y = x$$

Question 7

Evaluate $$\ln e^5$.

Accepted Answer

$$5$$

Question 8

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 9

If $$\log_5$ x = 3$$, what is the value of $$x$$?

Accepted Answer

$$125$$

Question 10

A function models the percentage of adult height attained by a boy as $$f(x) = 100 \log_{10}(0.2x + 0.6)$$, where $$x is $$age in years. Approximately what percentage of adult height has a boy attained at age 10?

Accepted Answer

$$80\%$$

Question 11

Which of the following is NOT a property of logarithms?

Accepted Answer

$$\log_b 1 = 1$$

Question 12

Given $$f(x) = \ln(x - 3)$$, what is the vertical asymptote of the graph?

Accepted Answer

$$x = 3$$

Question 13

Evaluate $$\log_6$ 36.$$

Accepted Answer

$$2$$

Question 14

Which of the following is the correct logarithmic form of the equation $$e^y = x$$?

Accepted Answer

$$y = \ln x$$

Question 15

If $$\log_{b} x is a $$decreasing function, which of the following must be true?

Accepted Answer

$$0 \u003c b \u003c 1$$

Question 16

The temperature increase in a car is modeled by $$f(x) = 43 \log_{10}(x + 1)$$, where $$x is $$minutes. What is the temperature increase after 30 minutes, to the nearest degree?

Accepted Answer

$$34$$

Question 17

Which of the following is the range of the function $$f(x) = \log_2$ x$$?

Accepted Answer

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

Question 18

Which equation is equivalent to $$\log_{10} x = 4$$?

Accepted Answer

$$x = 10^4$

Question 19

If $$\log_7$ x = 0$$, what is the value of $$x$$?

Accepted Answer

$$1$$

Question 20

Which of the following statements about the graph of $$f(x) = \log_b x is $$FALSE?

Accepted Answer

The graph passes through the origin $$(0, 0)$$

Exponential and Logarithmic Functions: Logarithmic Functions

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