Question 1

Solve the exponential equation $$2^{3x-1} = 16$.

Accepted Answer

$$x = 1$$

Question 2

Which property allows you to solve the equation $$5^x = 5^7$ by setting x = 7$?

Accepted Answer

The one-to-one property of exponents

Question 3

Solve for $$x$$: $$e^{2x} = 20$.

Accepted Answer

$$x = \frac{1}{2} \ln 20$$

Question 4

Which of the following is the correct first step to solve $$3^{x+1} = 7$?

Accepted Answer

Take the logarithm of both sides

Question 5

Solve for $$x$$: $$\log_{2}(x) = 5.$$

Accepted Answer

$$x = 2^5$

Question 6

Which of the following is NOT a valid solution for $$\log(x-2) = 1$$?

Accepted Answer

$$x = 2$$

Question 7

If $$\log_5$(x) = \log_5$(3x-4)$$, what is the solution for $$x$$?

Accepted Answer

$$x = 2$$

Question 8

Solve for $$x$$: $$\log(x+1) + \log(x-1) = 1.$$

Accepted Answer

$$x = 2$$

Question 9

A $$1000 investment grows to 3600 at 8$$% annual interest compounded quarterly. Which equation models the time $$t in $$years required for this growth?

Accepted Answer

$$3600 = 1000(1 + 0.08/4$$)^{4t}$$

Question 10

If $$\log_3$(x) = 2$$, what is the value of $$x$$?

Accepted Answer

$$x = 9$$

Question 11

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

Accepted Answer

$$x = \log_2$ 7$$

Question 12

Solve for $$x$$: $$\log_4$(x) = -2.$$

Accepted Answer

$$x = 1/4^2$

Question 13

Which of the following is a necessary condition for the solution of $$\log(x-3) = 2 to be $$valid?

Accepted Answer

$$x \u003e 3$$

Question 14

If $$\log_2$(x) = \log_2$(8)$$, what is $$x$$?

Accepted Answer

$$x = 8$$

Question 15

A girl’s adult height percentage is modeled by $$f(x) = 100 - 80e$$^{-0.16x}$$, where x$ is age in years. At what age does she reach 97% of her adult height?

Accepted Answer

$$x \approx 14$$

Question 16

Solve for $$x$$: $$\log_5$(x^2) = 2$.

Accepted Answer

$$x = \pm 5$$

Question 17

Which property is used to solve $$\log_3$(x) = \log_3$(2x-1)$$?

Accepted Answer

One-to-one property of logarithms

Question 18

Solve for $$x$$: $$\log(x+2) = \log(3x-4).$$

Accepted Answer

$$x = 2$$

Question 19

Which of the following is the correct solution for $$e^{x} = 15$?

Accepted Answer

$$x = \ln 15$$

Question 20

If $$\log(x) = 0$$, what is the value of $$x$$?

Accepted Answer

$$x = 1$$

Exponential and Logarithmic Equations: Study Notes for College Algebra

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