Question 1

Which property of logarithms allows you to write $$\log_b(MN) as$$ $$\log_b(M) + \log_b(N)$$?

Accepted Answer

Product Rule

Question 2

Expand the expression $$\log_2$(8x)$$ using properties of logarithms.

Accepted Answer

$$\log_2$(8) + \log_2$(x)$$

Question 3

Which of the following is the correct application of the quotient rule to $$\log_5$\left(\frac{a}{b}\right)$$?

Accepted Answer

$$\log_5$(a) - \log_5$(b)$$

Question 4

Condense the expression $$2\log_3$(x) + \log_3$(y)$$ into a single logarithm.

Accepted Answer

$$\log_3$(x^2y$$)$

Question 5

Expand $$\log_4$\left(\frac{x^3$y}{z^2$}\right) as $$much as possible.

Accepted Answer

$$3\log_4$(x) + \log_4$(y) - 2\log_4$(z)$$

Question 6

Which property allows you to write $$\log_b(M^p) as$$ $$p\log_b(M)$$?

Accepted Answer

Power Rule

Question 7

Write $$\log_7$(49)$$ using the power rule.

Accepted Answer

$$2\log_7$(7)$$

Question 8

Condense $$\log_2$(a) - 3\log_2$(b)$$ into a single logarithm.

Accepted Answer

$$\log_2$\left(\frac{a}{b^3$}\right)$$

Question 9

Use the change-of-base property to rewrite $$\log_5$(20) in $$terms of common logarithms.

Accepted Answer

$$\frac{\log_{10}(20)}{\log_{10}(5)}$$

Question 10

Evaluate $$\log_2$(32)$$ using properties of logarithms.

Accepted Answer

$$5$$

Question 11

Expand $$\log_6$(18x^2$$)$ as much as possible.

Accepted Answer

$$\log_6$(18) + 2\log_6$(x)$$

Question 12

Which of the following is equivalent to $$\log_3$(81)$$?

Accepted Answer

$$4$$

Question 13

A scientist needs to compare $$\log_{12}(144)$$ using natural logarithms. Which expression should they use?

Accepted Answer

$$\frac{\ln(144)}{\ln(12)}$$

Question 14

Expand $$\log_5$\left(\frac{25x^4$}{y}\right) as $$much as possible.

Accepted Answer

$$2\log_5$(5) + 4\log_5$(x) - \log_5$(y)$$

Question 15

Condense $$\log_7$(a) + \log_7$(b) - 2\log_7$(c)$$ into a single logarithm.

Accepted Answer

$$\log_7$\left(\frac{ab}{c^2$}\right)$$

Question 16

A chemist is analyzing a reaction where the concentration of a substance is modeled by $$\log_{10}(1000t)$$, where $$t is $$time in seconds. Expand this expression.

Accepted Answer

$$\log_{10}(1000) + \log_{10}(t)$$

Properties of Logarithms – College Algebra Study Notes

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