Question 1

Which property allows you to solve the equation $$2^x = 64 by $$setting the exponents equal to each other?

Accepted Answer

The one-to-one property of exponential functions

Question 2

Solve the equation $$2^{3x} = 9$ using logarithms. What is the value of x$?

Accepted Answer

$$x = \frac{\log 9}{3 \log 2}$$

Question 3

Given the equation $$\log_3$(x) + \log_3$(x-8) = 2$$, what is the solution for $$x$$?

Accepted Answer

$$x = 9$$

Question 4

Which of the following is the correct inverse function for $$A(t) = 1000e$$^{0.065t}$$?

Accepted Answer

$$A^{-1}(t$$) = \frac{\ln(\frac{t}{1000})}{0.065}$$

Question 5

If $$e^{2x} = 60$, what is the value of x$?

Accepted Answer

$$x = \frac{1}{2} \ln 60$$

Question 6

A bank account grows according to $$A(t) = 1000e$$^{0.065t}$$. How long will it take for the account to double?

Accepted Answer

$$t = \frac{\ln 2}{0.065}$$

Question 7

Which of the following best describes the solution method for $$e^{2x} - 3e^x - 4 = 0$?

Accepted Answer

Let $$y = e^x$$ and solve the resulting quadratic equation

Question 8

Solve the inequality $$5^x \u003e 125$$^{x+6}$$. Which of the following is correct?

Accepted Answer

$$x \u003c -2$$

Question 9

Which property allows you to conclude that if $$\log_b(u) = \log_b(v)$$, then $$u = v$$?

Accepted Answer

The one-to-one property of logarithmic functions

Question 10

Given $$\log_2$(4x) = 5$$, what is the value of $$x$$?

Accepted Answer

$$x = 8$$

Question 11

Which of the following is true about the function $$y = b^x if$$ $$0 \u003c b \u003c 1$$?

Accepted Answer

The function is decreasing for all $$x$$

Question 12

If $$\log_2$ 9 \u003e 2 \log_2$ x$$, what is the solution set for $$x$$?

Accepted Answer

$$x \u003c 3$$

Question 13

Which equation can be solved by first combining logarithms using the product property?

Accepted Answer

$$\log_x + \log(x+15) = 2$$

Question 14

If $$\log_{1/2}(2x-3) \geq \log_{1/2}(x+5)$$, what is the solution set for $$x$$?

Accepted Answer

$$x \leq 8$$

Question 15

Which of the following best describes the domain restriction when solving logarithmic equations?

Accepted Answer

The argument of the logarithm must be positive

Question 16

Given $$e^x = \pi$$^{1+x}$$, what is the value of x$?

Accepted Answer

$$x = \frac{\ln \pi}{1 - \ln \pi}$$

Question 17

If $$\log_3$ x + \log_3$(x-8) = 2$$, what must be true about $$x$$ before solving?

Accepted Answer

$$x \u003e 8$$

Question 18

Which of the following is the correct solution for $$2 \log_3$ x = 3 \log_3$ 4$$?

Accepted Answer

$$x = 64$$

Question 19

If $$A^{-1}(15$$)$$ is calculated for the function A(t$$) = $$1000e^{0.065t}$$, what does the result represent in context?

Accepted Answer

The time required for the account balance to reach $15

Exponential and Logarithmic Equations & Applications – Study Guidance

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