Question 1

Which property from the image allows you to rewrite $$\log_a(M \cdot N) as a $$sum of two logarithms?

Accepted Answer

$$\log_a(M \cdot N) = \log_a M + \log_a N$$

Question 2

According to the properties shown, what is the value of $$\log_a 1$$ for any valid base $$a$$?

Accepted Answer

$$0$$

Question 3

Which property from the image is used to expand $$\log_a\left(\frac{M}{N}\right)$$?

Accepted Answer

$$\log_a\left(\frac{M}{N}\right) = \log_a M - \log_a N$$

Question 4

If $$\log_a a = 1$$, what is the value of $$a$$?

Accepted Answer

Any positive number except 1

Question 5

Which property allows you to write $$a^{\log_a M} = M$?

Accepted Answer

$$a^{\log_a M} = M$

Question 6

Using the properties, how can $$\log_a M^r be $$rewritten?

Accepted Answer

$$r \log_a M$$

Question 7

Which property from the image is the change of base formula?

Accepted Answer

$$\log_a M = \frac{\log_s M}{\log_s a}$$

Question 8

If $$\log_2$ 8 = x$$, what is the value of $$x$$?

Accepted Answer

$$3$$

Question 9

Which property would you use to simplify $$\log_a a^r$$?

Accepted Answer

$$\log_a a^r = r$$

Question 10

Given $$\log_5$ 25 = x$$, use the properties to find $$x.$$

Accepted Answer

$$2$$

Logarithmic Functions and Their Properties: Study Guide

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