Question 1

Which of the following is equivalent to $$\log_3$ 81 = x in $$exponential form?

Accepted Answer

$$3^x = 81$$

Question 2

If $$\log_b 25 = 2$$, what is the value of $$b$$?

Accepted Answer

$$b = 5$$

Question 3

Which property of logarithms allows you to write $$\log_2$ (xy) as$$ $$\log_2$ x + \log_2$ y$$?

Accepted Answer

Product Rule

Question 4

Simplify $$\log_5$ 125$$ without using a calculator.

Accepted Answer

$$3$$

Question 5

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

Accepted Answer

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

Question 6

Condense the expression $$2 \log_3$ x - \dfrac{1}{2} \log_3$ y$$ into a single logarithm.

Accepted Answer

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

Question 7

Solve for $$x$$: $$\log_2$ (x - 1) = 3.$$

Accepted Answer

$$x = 9$$

Question 8

Evaluate $$\log_{10} 0.01$$ without a calculator.

Accepted Answer

$$-2$$

Question 9

Which of the following statements is TRUE?

Accepted Answer

$$\log_b b = 1$$

Question 10

Rewrite $$\log_2$ 8 + \log_2$ 4 as a $$single logarithm and evaluate.

Accepted Answer

$$\log_2$ 32 = 5$$

Question 11

If $$\log_5$ x = 3$$, what is the value of $$x$$?

Accepted Answer

$$125$$

Question 12

Which property justifies the equation $$\log_b (x^k) = k \log_b x$$?

Accepted Answer

Power Rule

Question 13

Solve for $$x$$: $$2^x = 20. $$Give your answer in terms of logarithms.

Accepted Answer

$$x = \dfrac{\log 20}{\log 2}$$

Question 14

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

Accepted Answer

$$\dfrac{\log 50}{\log 7}$$

Question 15

A scientist is studying bacteria growth modeled by $$y = ab^x. If $$the population doubles every 3 hours, which equation represents this situation?

Accepted Answer

$$y = a \cdot 2$$^{x/3}$$

Question 16

Evaluate $$\log_4$ 1.$$

Accepted Answer

$$0$$

Question 17

Which of the following is equivalent to $$e^{\ln x}$$?

Accepted Answer

$$x$$

Question 18

Condense $$\log_2$ x + 3 \log_2$ y - \dfrac{1}{2} \log_2$ z$$ into a single logarithm.

Accepted Answer

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

Question 19

Solve for $$x$$: $$\log_3$ (x + 2) = 4.$$

Accepted Answer

$$x = 79$$

C4

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