Question 1

Which of the following is the correct solution to the equation $$5^{3x-6} = 125$?

Accepted Answer

$$x = 3$$

Question 2

Solve the equation $$8^{x+2}$$ = $$4^{x-3} by $$expressing both sides as powers of the same base.

Accepted Answer

$$x = -12$$

Question 3

What is the solution to $$4^x = 15$$ using logarithms?

Accepted Answer

$$x = \frac{\ln 15}{\ln 4}$$

Question 4

Solve $$7e^{2x} - 5 = 58$ for x$.

Accepted Answer

$$x = \frac{\ln 9}{2}$$

Question 5

Which of the following is the solution to $$5^{x-2}$$ = $$4^{2x+3}$$?

Accepted Answer

$$x = \frac{2\ln 5 + 3\ln 4}{\ln 5 - 2\ln 4}$$

Question 6

Solve $$e^{2x} - 8e^x + 7 = 0$ for x$.

Accepted Answer

$$x = 0 or$$ $$x = \ln 7$$

Question 7

What is the solution to $$\log_2$(x-4) = 3$$?

Accepted Answer

$$x = 12$$

Question 8

Solve $$4\ln(3x) = 8$$ for $$x.$$

Accepted Answer

$$x = \frac{e^2$}{3}$$

Question 9

Given $$\log x + \log(x-3) = 1$$, which value(s) of $$x$$ are valid solutions?

Accepted Answer

$$x = 5$$

Question 10

Solve $$\ln(x-3) = \ln(7x-23) - \ln(x+1)$$ for $$x.$$

Accepted Answer

$$x = 4 or$$ $$x = 5$$

Question 11

The population of Florida is modeled by $$A = 15.9e$$^{0.0235t}$$, where A$ is in millions and t$ is years after 2000. What was the population in 2000?

Accepted Answer

$$15.9$$ million

Question 12

Using the population model $$A = 15.9e$$^{0.0235t}$$, in what year will the population reach 19.2$ million?

Accepted Answer

2008

Question 13

Which property allows you to solve $$\log_b M = \log_b N by $$setting $$M = N$$?

Accepted Answer

One-to-one property of logarithms

Question 14

If $$\log x + \log(x-3) = 1$$, what is the first step to solve for $$x$$?

Accepted Answer

Combine using the product rule: $$\log[x(x-3)] = 1$$

Question 15

Which of the following is NOT a valid solution to $$\log_2$(x-4) = 3$$?

Accepted Answer

$$x = 4$$

Question 16

What is the solution to $$e^{2x} - 8e^x + 7 = 0$ after substituting y = e^x$?

Accepted Answer

$$y = 1 or$$ $$y = 7$$

Question 17

If $$\log_b M = C$$, what is the equivalent exponential form?

Accepted Answer

$$b^C = M$$

Question 18

Which step is necessary when solving logarithmic equations to ensure the solution is valid?

Accepted Answer

Check that the argument of the logarithm is positive

Question 19

Which equation would you solve using the natural logarithm rather than the common logarithm?

Accepted Answer

$$e^{2x} = 9$

Solving Exponential and Logarithmic Equations (Precalculus Study Guide)

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