Q: A $$\5000$ investment grows at an annual rate of 6$$\%$$ compounded quarterly. What is the value after 5 years? Use A = P(1$$ + \frac{r}{n}$$)^{nt}$.

$$5000(1 + \frac{0.06}{4}$$)^{4 \times 5}$$ \approx \6$$,720$

Question 1

Which of the following is the correct exponential inverse of the equation $$y = 5 	imes 2^x$$?

Accepted Answer

$$x = \log_2$(y/5)$$

Question 2

A population of bacteria triples every 4 hours. If the initial population is 200, what will the population be after 12 hours?

Accepted Answer

$$200 	imes 3^3$ = 5400$$

Question 3

Which of the following is the correct simplification of $$\sqrt[3]{\dfrac{27x^7$y^2$$}{$$3x^2y^5$}}$$?

Accepted Answer

$$3x^{5/3}y$$^{-1}$

Question 4

If $$2x^2 + 2x - 8 = 0$, what are the zeros of the expression?

Accepted Answer

Question 5

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

Accepted Answer

Product property of logarithms

Question 6

A $$\5000$ investment grows at an annual rate of 6$$\%$$ compounded quarterly. What is the value after 5 years? Use A = P(1$$ + \frac{r}{n}$$)^{nt}$.

Accepted Answer

$$5000(1 + \frac{0.06}{4}$$)^{4 	imes 5}$$ \approx \6$$,720$

Question 7

Solve for $$x$$: $$3^{2x-1} = 81$.

Accepted Answer

$$x = 2$$

Question 8

Which of the following is the correct logarithmic form of the exponential equation $$7^x = 50$$?

Accepted Answer

$$x = \log_7$(50)$$

Question 9

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

Accepted Answer

$$x = 32$$

Question 10

Which of the following is the correct application of the one-to-one property to solve $$9^x = 81$$?

Accepted Answer

$$x = 2$$

Question 11

Simplify the radical expression $$\sqrt{50x^4$y^2$$}$.

Accepted Answer

$$5x^2y$$\sqrt{2}$$

Question 12

Which of the following is the correct solution for $$e^{2x} = 7$?

Accepted Answer

$$x = \frac{1}{2}\ln(7)$$

Question 13

Find the zeros of the logarithmic expression $$\log_3$(x^2 - 4) = 0$.

Accepted Answer

$$x = 2, x = -2$$

Question 14

Which of the following is the correct simplification of $$\dfrac{2x^3$y^2$$}{$$4x^2y^5$}$$?

Accepted Answer

$$\dfrac{x}{2y^3$}$$

Question 15

A radioactive substance decays according to $$A = A_0e$$^{-kt}$$. If A_0$ = 100$$ grams, $$k = 0.05$$, and $$t = 10$$ years, what is the remaining amount?

Accepted Answer

$$100e^{-0.5}$$ \approx 60.65$$ grams

Question 16

Which of the following is the correct application of the power property to $$\log_5$(x^3$$)$?

Accepted Answer

$$3\log_5$(x)$$

Question 17

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

Accepted Answer

$$100$$

Question 18

Which of the following is the correct exponential form of $$\log_4$(64) = x$$?

Accepted Answer

$$4^x = 64$$

Question 19

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

Accepted Answer

$$x = 9$$

Question 20

Which of the following is the correct simplification of $$\sqrt[4]{16x^8$y^{12}$$}$?

Accepted Answer

$$2x^2y^3$

Precalculus Study Guide: Exponential and Logarithmic Equations

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