Question 1

Which of the following best describes the meaning of $$\log_b(a) = k$$?

Accepted Answer

$$b^k = a$$

Question 2

Evaluate $$\log(100).$$

Accepted Answer

$$2$$

Question 3

Estimate $$\log(2.372)$$ using the provided log table.

Accepted Answer

$$0.375$$

Question 4

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

Accepted Answer

$$\log_b(a) + \log_b(c)$$

Question 5

Given $$\log(2) \approx 0.3$$, evaluate $$\log(20).$$

Accepted Answer

$$1.3$$

Question 6

Evaluate $$\log(0.001).$$

Accepted Answer

$$-3$$

Question 7

If $$\log(2) \approx 0.3$$, what is $$\log(200)$$?

Accepted Answer

$$2.3$$

Question 8

Using the product property, evaluate $$\log(100 	imes 1000).$$

Accepted Answer

$$5$$

Question 9

Given $$\log(2) \approx 0.3$$, evaluate $$\log(0.002).$$

Accepted Answer

$$-2.7$$

Question 10

If $$\log(2) \approx 0.3$$, what is $$\log(2 	imes 10^x) in $$terms of $$x$$?

Accepted Answer

$$x + 0.3$$

Question 11

Which of the following is the correct value for $$\log(10,000)$$?

Accepted Answer

$$4$$

Question 12

Suppose you are a chemist and need to calculate the pH of a solution with $$[H^+] = 2.0 	imes 10$$^{-4}$$ M. What is the pH?

Accepted Answer

$$3.7$$

Question 13

Which of the following is the inverse function of $$y = 10^x$$?

Accepted Answer

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

Question 14

If $$\log_{10}(x) = 0.4771$$, what is $$x$$?

Accepted Answer

$$3$$

Question 15

A sound has an intensity of $$I = 2.0 	imes 10$$^{-5}$$ W/m^2$. The sound level in decibels is given by L = 10$$ \log_{10}($$I/I_0$$)$$, where I_0$ = 1.0 	imes 10$$^{-12}$$ W/m^2$. What is L$?

Accepted Answer

$$77 dB$$

Lecture 10: Logarithms: Properties, Evaluation, and Applications

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