Question 1

Solve for $$x$$: $$2 \log_2$(x) + 3 = 0$$

Accepted Answer

$$x = 2$$^{-1.5}$$ = \dfrac{1}{2\sqrt{2}}$$

Question 2

Which of the following is the solution to $$\log_2$(x) + \log_2$(2x+1) = 0$$?

Accepted Answer

$$x = \dfrac{1}{2}$$

Question 3

Given $$\log_7$(x-1) = 2\log_7$(x-1)$$, what is the solution for $$x$$?

Accepted Answer

No solution

Question 4

Solve for $$x$$: $$2\ln(x+3) = \ln(x+1) + 3\ln2$$

Accepted Answer

$$x = 5$$

Question 5

If $$\log_2$(2x-9) = 2 - \log_2$(x-1)$$, what is the value of $$x$$?

Accepted Answer

$$x = 5$$

Question 6

Solve for $$x$$: $$\log_2$((x-2)(x-3)) = \log_2$ 9$$

Accepted Answer

$$x = 5 or$$ $$x = -1$$

Question 7

What is the solution to $$\log_3$\left(\dfrac{x}{3}\right) = 2$$?

Accepted Answer

$$x = 27$$

Question 8

A biologist models bacteria growth with $$N = N_0$ e$$^{kt}$$. If N_0$ = 100$$, $$N = 800$$ after 6 hours, what is the value of $$k$$? (Round to 3 decimal places)

Accepted Answer

$$k = 0.231$$

Question 9

A radioactive substance decays according to $$A = A_0$ e$$^{-0.05t}$$. How long will it take for the substance to decay to 25% of its original amount?

Accepted Answer

$$t = 27.73$$

Question 10

If $$\log_b(x) = 3$$ and $$\log_b(y) = 2$$, what is $$\log_b\left(\dfrac{x^2$}{y^3$}\right)$$?

Accepted Answer

$$6 - 6 = 0$$

Question 11

Which of the following is equivalent to $$\log_5$(25x)$$?

Accepted Answer

$$2 + \log_5$(x)$$

Question 12

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

Accepted Answer

$$x = 16$$

Question 13

Solve for $$x$$: $$\ln(x^2$) = 6$$

Accepted Answer

$$x = \pm e^3$

Question 14

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

Accepted Answer

$$x = 0.01$$

Question 15

Which of the following is the correct domain for $$f(x) = \log_2$(x-4)$$?

Accepted Answer

$$x \u003e 4$$

Question 16

A population doubles every 5 years. If the initial population is 1000, what will it be after 15 years?

Accepted Answer

$$4000$$

Question 17

If $$\log_3$(x) = 5$$, what is $$\log_3$(\sqrt{x})$$?

Accepted Answer

$$2.5$$

Question 18

Which property allows you to write $$\log_b(MN) = \log_b(M) + \log_b(N)$$?

Accepted Answer

Product Property of Logarithms

Question 19

If $$\log_4$(x) = 3$$, what is $$x$$?

Accepted Answer

$$x = 64$$

Question 20

Solve for $$x$$: $$\log_2$(x) + \log_2$(x-2) = 3$$

Accepted Answer

$$x = 4$$

Solving Logarithmic Equations in College Algebra

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