Question 1

Which of the following is the correct logarithmic form of the exponential equation $$2^x = 8$$?

Accepted Answer

$$\log_2$ 8 = x$$

Question 2

Solve the exponential equation $$3^{2x-1} = 27$. What is the value of x$?

Accepted Answer

Question 3

What is the domain of the logarithmic function $$f(x) = \log_2$(x-3)$$?

Accepted Answer

$$x \u003e 3$$

Question 4

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

Accepted Answer

The graph of $$g(x) is $$the reflection of $$f(x)$$ across the line $$y = x$$

Question 5

Which property allows you to write $$\log_b a = \frac{\log_c a}{\log_c b}$$?

Accepted Answer

Change of Base Property

Question 6

Solve the logarithmic equation $$\log_3$(x-2) = 2. $$What is $$x$$?

Accepted Answer

$$x = 11$$

Question 7

Which of the following is the correct exponential form of $$\log_5$ x = 3$$?

Accepted Answer

$$x = 5^3$

Question 8

A population of 1000 bacteria doubles every hour. How many bacteria will there be after 5 hours?

Accepted Answer

$$16,000$$

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

The graph has a vertical asymptote at $$x = 0$$

Question 11

Solve the equation $$2^{x+1} = 16$ for x$.

Accepted Answer

$$x = 3$$

Question 12

Which of the following is undefined for logarithmic functions?

Accepted Answer

The logarithm of a negative number

Question 13

If $$f(x) = \log_2$(x+1) - 3$$, what is the vertical shift of the graph?

Accepted Answer

Down 3 units

Question 14

Which of the following is the inverse function of $$f(x) = 2^x$$?

Accepted Answer

$$f^{-1}(x$$) = \$$log_2 x$

Question 15

What is the solution to $$\log_4$(x+5) = 2$$?

Accepted Answer

$$x = 11$$

Question 16

Which of the following is the correct domain for $$f(x) = \log_3$(x-1)$$?

Accepted Answer

$$x \u003e 1$$

Question 17

If $$f(x) = \log_2$ x$$ and $$g(x) = \log_2$(x-4)$$, what is the horizontal shift between the two graphs?

Accepted Answer

Right 4 units

Question 18

Which of the following is the correct exponential form of $$\log_7$ 49 = x$$?

Accepted Answer

$$7^x = 49$$

Question 19

Solve the equation $$5^{x-2} = 125$ for x$.

Accepted Answer

$$x = 4$$

Question 20

Which of the following is the correct range for $$f(x) = 2^x$$?

Accepted Answer

$$(0, \infty)$$

Exponential and Logarithmic Functions: Solving Equations and Graphs

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