Question 1

Which of the following correctly expresses $$\log_2$(32)$$?

Accepted Answer

$$\log_2$(32) = 5$$

Question 2

What is the value of $$\log_3$(81)$$?

Accepted Answer

$$\log_3$(81) = 4$$

Question 3

Simplify $$\ln\$$left((e^{3x}$$ 	imes e$$^{y}$$)^2$$ight)$.

Accepted Answer

$$6x + 2y$$

Question 4

Which of the following is equivalent to $$\log_2$\left(\frac{1}{8}\right)$$?

Accepted Answer

$$-3$$

Question 5

If $$\log_5$(25) = x$$, what is the value of $$x$$?

Accepted Answer

$$x = 2$$

Question 6

A scientist measures the pH of a solution as 3. What is the hydrogen ion concentration $$[H^+]$$? (Recall $$	ext{pH} = -\log_{10}[H^+])$$

Accepted Answer

$$[H^+] = 10$$^{-3}$$

Question 7

Which property of logarithms allows you to write $$\log_b(xy) as$$ $$\log_b(x) + \log_b(y)$$?

Accepted Answer

Product Rule

Question 8

Simplify $$\log_2$(16) + \log_2$(8).$$

Accepted Answer

$$7$$

Question 9

Which of the following is equivalent to $$\log_5$(25) + \log_5$(5)$$?

Accepted Answer

$$3$$

Question 10

A medical researcher models bacterial growth with $$N(t) = N_0$ e$$^{kt}$$. If N_0$ = 100$$, $$k = 0.5$$, and $$t = 4$$, what is $$\ln(N(4))$$?

Accepted Answer

$$\ln(100) + 2$$

Question 11

Which of the following is the correct simplification of $$\log_3$(9^2$$)$?

Accepted Answer

$$4$$

Question 12

If $$\log_b(a) = x$$, which of the following is true?

Accepted Answer

$$b^x = a$$

Question 13

A radioactive substance decays according to $$A(t) = A_0$ e$$^{-kt}$$. If A_0$ = 50$$, $$k = 0.1$$, and $$t = 10$$, what is $$\ln(A(10))$$?

Accepted Answer

$$\ln(50) - 1$$

Question 14

Which of the following is equivalent to $$\log_2$(16) - \log_2$(2)$$?

Accepted Answer

$$3$$

Question 15

If $$\log_2$(x) = 5$$, what is $$x$$?

Accepted Answer

$$32$$

Question 16

Which of the following is the correct simplification of $$\ln(e$$^{3x + y}$$)$$?

Accepted Answer

$$3x + y$$

Question 17

A population doubles every 5 years. If the population at time $$t is$$ $$P(t) = P_0$ 	imes 2$$^{t/5}$$, what is $$\$$log_2(P(10$$)/$$P_0$$)$$?

Accepted Answer

$$2$$

Question 18

Which of the following is equivalent to $$\log_2$(16) 	imes \log_2$(2)$$?

Accepted Answer

$$8$$

Question 19

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

Accepted Answer

$$9$$

Question 20

Which of the following is the correct simplification of $$\ln(e$$^{x}$$ \cdot e$$^{2y}$$)$$?

Accepted Answer

$$x + 2y$$

Lecture 14: Logarithms: Properties, Bases, and Simplification

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