Question 1

Given the function $$f(x) = x^2$ - 2$$, what are the coordinates of its vertex?

Accepted Answer

$$(0, -2)$$

Question 2

Which of the following is the equation of the asymptote for the function $$f(x) = \log_3$(x-2)$$?

Accepted Answer

$$x = 2$$

Question 3

Express the exponential equation $$3^x = 12 in $$logarithmic form.

Accepted Answer

$$x = \log_3$ 12$$

Question 4

Evaluate $$\log_3$ 81.$$

Accepted Answer

$$4$$

Question 5

Simplify $$\log_5$ 125.$$

Accepted Answer

$$3$$

Question 6

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

Accepted Answer

Product Property

Question 7

Rewrite $$\log_2$ 8$$ using the change of base formula.

Accepted Answer

$$\dfrac{\log 8}{\log 2}$$

Question 8

Solve for $$x$$: $$2x + 3\log_3$ x = 12. $$Round your answer to two decimal places.

Accepted Answer

$$x \approx 2.36$$

Question 9

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

Accepted Answer

$$32$$

Question 10

Which of the following correctly simplifies $$\log_2$ 8 - \log_2$ 4$$?

Accepted Answer

$$1$$

Question 11

A population of bacteria triples every 5 hours. If you start with 100 bacteria, how many will you have after 15 hours?

Accepted Answer

$$2700$$

Question 12

The formula for compound interest is $$A = P(1 + r/n$$)^{nt}$$. If you invest P = 1000$ at r = 0.05$ compounded annually for t = 3$ years, what is A$?

Accepted Answer

$$1157.63$$

Question 13

Which equation represents exponential decay?

Accepted Answer

$$y = 100e$$^{-0.2x}$$

Question 14

If $$\log_5$ x = 3$$, what is $$x$$?

Accepted Answer

$$125$$

Question 15

Which of the following is equivalent to $$\log_2$ 32$$?

Accepted Answer

$$5$$

Question 16

A radioactive substance decays according to $$A = A_0$ e$$^{-kt}$$. If A_0$ = 50$$ grams and $$k = 0.1$$, how much remains after $$t = 20$$ hours? (Round to two decimal places)

Accepted Answer

$$6.77$$ grams

Question 17

Which of the following is the correct application of the power property of logarithms to $$\log_2$ 8^3$?

Accepted Answer

$$3 \log_2$ 8$$

Question 18

If $$\log_3$ x = 2$$, what is $$x$$?

Accepted Answer

$$9$$

Question 19

Which of the following is the correct simplification of $$\log_2$ 16 - \log_2$ 2$$?

Accepted Answer

$$3$$

Question 20

A medication is administered and its concentration in the bloodstream decreases exponentially according to $$C = C_0$ e$$^{-0.3t}$$, where C_0$ = 100 mg. $$How much remains after $$t = 5$$ hours? (Round to nearest mg)

Accepted Answer

$$22 mg$$

Exponential and Logarithmic Functions: Study Guide and Practice Problems

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