$$y = \log_b(x)$$ \text{ is defined as the inverse of } y = b^x$

Question 1

Which of the following is the correct definition of the logarithmic function with base $$b \u003e 0$$, $$b 
eq 1$$?

Accepted Answer

$$y = \log_b(x)$$ 	ext{ is defined as the inverse of } y = b^x$

Question 2

What is the domain of the function $$f(x) = \log_3$(x-2)$$?

Accepted Answer

$$x \u003e 2$$

Question 3

Which property of logarithms allows you to write $$\log_b(xy) as a $$sum?

Accepted Answer

$$\log_b(xy) = \log_b(x) + \log_b(y)$$

Question 4

If $$f(x) = \log_2$(x)$$, what is the vertical asymptote of its graph?

Accepted Answer

$$x = 0$$

Question 5

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

Accepted Answer

The graph is increasing on $$(0, \infty)$$

Question 6

What is the value of $$\log_5$(1)$$?

Accepted Answer

$$0$$

Question 7

Which of the following is the correct cancellation property for logarithms?

Accepted Answer

$$b^{\log_b(x)} = x$

Question 8

If $$\log_b(x) = y$$, which equation is equivalent?

Accepted Answer

$$b^y = x$$

Question 9

Which of the following is the natural logarithmic function?

Accepted Answer

$$y = \ln(x)$$

Question 10

What is the range of the function $$f(x) = \log_4$(x)$$?

Accepted Answer

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

Question 11

A scientist measures the pH of a solution as $$pH = -\log_{10}([H^+]). If$$ $$[H^+] = 10$$^{-7}$$, what is the pH?

Accepted Answer

$$7$$

Question 12

Which transformation shifts the graph of $$f(x) = \log_2$(x)$$ one unit to the right?

Accepted Answer

$$f(x) = \log_2$(x-1)$$

Question 13

If $$f(x) = \log_3$(x)$$, which point does the graph always pass through?

Accepted Answer

$$(1, 0)$$

Question 14

Which of the following is equivalent to $$\log_b(x^r)$$?

Accepted Answer

$$r \log_b(x)$$

Question 15

A population grows exponentially according to $$P(t) = 1000 \cdot 2^t. $$What is the inverse function that gives $$t in $$terms of $$P$$?

Accepted Answer

$$t = \log_2$\left(\frac{P}{1000}\right)$$

Question 16

Which of the following is NOT a property of logarithms?

Accepted Answer

$$\log_b(x+y) = \log_b(x) + \log_b(y)$$

Question 17

If $$f(x) = \log_5$(x+2)$$, what is the domain of $$f$$?

Accepted Answer

$$x \u003e -2$$

Question 18

Which of the following is the correct definition of the common logarithm?

Accepted Answer

$$\log_{10}(x)$$

Question 19

If $$f(x) = \log_2$(x)$$ and $$g(x) = \log_2$(x-3)$$, how is the graph of $$g(x)$$ related to $$f(x)$$?

Accepted Answer

It is shifted 3 units to the right

Question 20

Which of the following is the correct way to find the domain of $$f(x) = \log_b(h(x))$$?

Accepted Answer

Solve $$h(x) \u003e 0$$

Logarithmic Functions: Definitions, Properties, and Graphs

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