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 $$\log_2$(8x^3$$)$ using properties of logarithms.

Accepted Answer

$$\log_2$(8) + 3\log_2$(x)$$

Question 3

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

Accepted Answer

$$\log_3$\left(\dfrac{x^2$}{y}\right)$$

Question 4

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

Accepted Answer

$$\log_b(M^p) = p\log_b(M)$$

Question 5

Expand $$\log_5$\left(\dfrac{25x^3$}{y^2$}\right) as a $$sum or difference of logarithms.

Accepted Answer

$$\log_5$(25) + 3\log_5$(x) - 2\log_5$(y)$$

Question 6

A scientist needs to evaluate $$\log_{12}(17)$$ using a calculator. Which formula should they use?

Accepted Answer

$$\dfrac{\log_{10}(17)}{\log_{10}(12)}$$

Question 7

Which of the following is equivalent to $$\log_2$(2x) + \log_2$(4)$$?

Accepted Answer

$$\log_2$(8x)$$

Question 8

If $$\log_b(5) = 0.7$$ and $$\log_b(2) = 0.3$$, what is $$\log_b(20)$$?

Accepted Answer

$$1.3$$

Question 9

Which property allows you to write $$\log_b\left(\dfrac{M}{N}\right) as a $$difference of logs?

Accepted Answer

Quotient Rule

Question 10

Condense the expression $$\log_7$(x) + \log_7$(y) - \log_7$(z)$$ into a single logarithm.

Accepted Answer

$$\log_7$\left(\dfrac{xy}{z}\right)$$

Question 11

Expand $$\log_3$(27x^2$$)$ as a sum of logarithms.

Accepted Answer

$$\log_3$(27) + 2\log_3$(x)$$

Question 12

A medical researcher uses $$\log_{10}(x) to $$model the pH of a solution. If the concentration changes from $$x to$$ $$10x$$, how does the pH change?

Accepted Answer

It increases by 1

Question 13

Evaluate $$\log_4$(64)$$ using properties of logarithms.

Accepted Answer

$$3$$

Question 14

Which of the following is the correct change of base formula for $$\log_7$(50)$$?

Accepted Answer

$$\dfrac{\log_{10}(50)}{\log_{10}(7)}$$

Question 15

Expand $$\log_2$\left(\dfrac{8x^4$}{y^3$}\right) as a $$sum or difference of logarithms.

Accepted Answer

$$\log_2$(8) + 4\log_2$(x) - 3\log_2$(y)$$

Question 16

If $$\log_{10}(x) = 2$$, what is the value of $$x$$?

Accepted Answer

$$100$$

Question 17

Condense the expression $$3\log_2$(a) + \log_2$(b) - 2\log_2$(c)$$ into a single logarithm.

Accepted Answer

$$\log_2$\left(\dfrac{a^3$b}{c^2$}\right)$$

Question 18

A chemist needs to evaluate $$\log_{e}(41)$$ using a calculator. Which formula should they use?

Accepted Answer

$$\dfrac{\ln(41)}{\ln(e)}$$

Question 19

Expand $$\log_6$(36x^5$$)$ as a sum of logarithms.

Accepted Answer

$$\log_6$(36) + 5\log_6$(x)$$

Properties of Logarithms: Product, Quotient, and Power Rules

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