Question 1

Which of the following statements best describes the relationship between exponential and logarithmic functions?

Accepted Answer

Logarithmic functions are the inverses of exponential functions.

Question 2

Given the function $$f(x) = 2^x$$, what is the equivalent logarithmic form for $$x = 2^y$$?

Accepted Answer

$$y = \log_2$ x$$

Question 3

Which of the following is the domain of the logarithmic function $$y = \log_b x$$ for $$b \u003e 0$$ and $$b 
eq 1$$?

Accepted Answer

All positive real numbers

Question 4

If $$\log_6$ x = 5$$, what is the value of $$x$$?

Accepted Answer

$$x = 7776$$

Question 5

Which of the following calculator entries will result in an error?

Accepted Answer

$$\log(-2.88)$$

Question 6

Convert the logarithmic equation $$2 = \log_b 100 to $$its equivalent exponential form.

Accepted Answer

$$b^2 = 100$

Question 7

Solve for $$x in $$the equation $$\log x = -1.864. $$Round your answer to four decimal places.

Accepted Answer

$$x = 0.0137$$

Question 8

Which of the following best describes a one-to-one function?

Accepted Answer

A function where each range value corresponds to exactly one domain value.

Question 9

Given the exponential equation $$10^x = 15$$, solve for $$x to $$four decimal places.

Accepted Answer

$$x = 1.1761$$

Question 10

Which of the following is the correct natural logarithm equation for $$x = e$$^{3.416}$$?

Accepted Answer

$$\ln x = 3.416$$

Question 11

If $$f(x) = \frac{x}{2}$$ and $$g(x) = \frac{|x|}{2}$$, which function is one-to-one?

Accepted Answer

$$f(x)$$ only

Question 12

Which of the following is the correct change of base formula for $$\log_b x$$?

Accepted Answer

$$\log_b x = \frac{\log x}{\log b}$$

Question 13

A company uses the model $$y = 256.4659 - 24.038 \ln x to $$predict price $$y$$ based on sales $$x. $$What is the predicted price when $$x = 6000 ($$rounded to the nearest dollar)?

Accepted Answer

$$47$$

Question 14

Which of the following is NOT a property of logarithmic functions?

Accepted Answer

The logarithmic function is defined for negative numbers.

Question 15

If $$\ln x = 3.416$$, what is the value of $$x to $$four decimal places?

Accepted Answer

$$x = 30.4474$$

Question 16

Which of the following real-world phenomena can be modeled using logarithmic functions?

Accepted Answer

The Richter scale for earthquakes

Question 17

If $$5^x = 11$$, solve for $$x to $$four decimal places.

Accepted Answer

$$x = 1.4899$$

Question 18

Which of the following is the correct exponential form of $$y = \log_3$ x$$?

Accepted Answer

$$x = 3^y$$

Question 19

Which of the following best describes the range of the exponential function $$y = 2^x$$?

Accepted Answer

All positive real numbers

Question 20

If an investment grows at 15% compounded annually, how long will it take to double? (Use $$\ln 2 = 0.6931$$ and $$\ln 1.15 = 0.1398$$; round to the next whole year.)

Accepted Answer

$$5$$ years

Logarithmic Functions: Definitions, Properties, and Applications 1.6

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