Question 1

Solve the exponential equation $$2^{x+1} = 16$. What is the value of x$?

Accepted Answer

$$x = 3$$

Question 2

Which of the following is the correct first step to solve the equation $$5^{2x} = 125$?

Accepted Answer

Rewrite $$125 as$$ $$5^3$$

Question 3

Solve for $$x$$: $$e^{3x} = 20$

Accepted Answer

$$x = \frac{1}{3} \ln 20$$

Question 4

Which property allows you to solve $$\log_2$(x) = \log_2$(7) by $$setting $$x = 7$$?

Accepted Answer

One-to-one property of logarithms

Question 5

Solve for $$x$$: $$\log_{10}(x-2) = 1$$

Accepted Answer

$$x = 12$$

Question 6

If $$\log_3$(x) = 4$$, what is the value of $$x$$?

Accepted Answer

$$x = 81$$

Question 7

Which equation is equivalent to $$7^{x} = 50$?

Accepted Answer

$$x = \log_7$ 50$$

Question 8

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

Accepted Answer

$$x = 4$$

Question 9

A $$1000 investment grows to 3600 at 8$$% annual interest compounded quarterly. Which equation would you use to solve for the time $$t in $$years?

Accepted Answer

$$3600 = 1000 \left(1 + \frac{0.08}{4}\$$right)^{4t}$$

Question 10

If $$\log_5$(x) = 2$$, what is $$x$$?

Accepted Answer

$$x = 25$$

Question 11

Solve for $$x$$: $$3^{2x-1} = 27$

Accepted Answer

$$x = 2$$

Question 12

Which of the following is the correct solution to $$\ln(x+1) = 2$$?

Accepted Answer

$$x = e^2$ - 1$$

Question 13

A girl has attained 97% of her adult height at age 14. If her adult height is $$H$$, what equation represents her height $$h at $$age 14?

Accepted Answer

$$h = 0.97H$$

Question 14

Which of the following is a valid step in solving $$4^{x} = 9$?

Accepted Answer

Take the natural logarithm of both sides: $$\ln 4$$^{x}$$ = \ln 9$$

Question 15

Solve for $$x$$: $$\log_2$(3x-1) = 4$$

Accepted Answer

$$x = 5$$

Question 16

Which of the following best describes the definition of a logarithm?

Accepted Answer

$$y = \log_b x$$ means $$b^y = x$$

Question 17

Which equation would you use to solve for $$x in$$ $$10^{2x} = 500$?

Accepted Answer

$$2x = \log_{10} 500$$

Question 18

Solve for $$x$$: $$\log_3$(x) = 1 + \log_3$(4)$$

Accepted Answer

$$x = 12$$

Question 19

Which of the following is the correct solution for $$2^{x+2} = 32$?

Accepted Answer

$$x = 3$$

Question 20

If $$\log_{b}(x) = y$$, which of the following is true?

Accepted Answer

$$b^{y} = x$

Exponential and Logarithmic Equations: Study Notes for College Algebra

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