Question 1

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

Accepted Answer

Product Rule

Question 2

Simplify the expression $$\log_3$(9x)$$ using properties of logarithms.

Accepted Answer

$$\log_3$ 9 + \log_3$ x$$

Question 3

Rewrite $$2\log_5$ x - \log_5$ y as a $$single logarithm.

Accepted Answer

$$\log_5$\left(\dfrac{x^2$}{y}\right)$$

Question 4

Which of the following is equivalent to $$\log_2$ 8$$?

Accepted Answer

$$3$$

Question 5

Expand $$\log_4$\left(\dfrac{16x^3$}{y^2$}\right)$$ using properties of logarithms.

Accepted Answer

$$\log_4$ 16 + 3\log_4$ x - 2\log_4$ y$$

Question 6

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

Accepted Answer

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

Question 7

Evaluate $$\log_{10} 1000$$ using properties of logarithms.

Accepted Answer

$$3$$

Question 8

Which property allows you to write $$k\log_b x as a $$single logarithm?

Accepted Answer

Power Rule

Question 9

Use the change of base formula to rewrite $$\log_5$ 17 in $$terms of common logarithms.

Accepted Answer

$$\dfrac{\log_{10} 17}{\log_{10} 5}$$

Question 10

If $$\log_2$ x = 5$$, what is the value of $$x$$?

Accepted Answer

$$32$$

Question 11

Expand $$\log_3$(2x^2y$$)$ as a sum of logarithms.

Accepted Answer

$$\log_3$ 2 + 2\log_3$ x + \log_3$ y$$

Question 12

Which of the following is the correct application of the quotient rule for logarithms?

Accepted Answer

$$\log_b\left(\dfrac{M}{N}\right) = \log_b M - \log_b N$$

Question 13

A scientist needs to calculate $$\log_{12} 50$$ but her calculator only has natural log and common log buttons. Which formula should she use?

Accepted Answer

$$\log_{12} 50 = \dfrac{\ln 50}{\ln 12}$$

Question 14

Condense $$3\log_2$ x + \log_2$ y - \log_2$ z$$ into a single logarithm.

Accepted Answer

$$\log_2$\left(\dfrac{x^3$y}{z}\right)$$

Question 15

Expand $$\log_6$\left(\dfrac{a^2$b^3$$}{$$c^4$$}\right)$ as a sum and/or difference of logarithms.

Accepted Answer

$$2\log_6$ a + 3\log_6$ b - 4\log_6$ c$$

Question 16

If $$\log_b x = 2$$ and $$\log_b y = 3$$, what is $$\log_b(x^2$y)$$?

Accepted Answer

$$7$$

Question 17

Which of the following is NOT a valid property of logarithms?

Accepted Answer

$$\log_b(M+N) = \log_b M + \log_b N$$

Properties of Logarithms: Product, Quotient, and Power Rules

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