Question 1

Which of the following is equivalent to $$\log_3$ 81 = x in $$exponential form?

Accepted Answer

$$3^x = 81$$

Question 2

Evaluate $$\log_5$ 1$$ without using a calculator.

Accepted Answer

$$0$$

Question 3

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

Accepted Answer

Product Rule

Question 4

Expand the expression $$\log_2$ \left( \dfrac{8x^3$}{y} \right)$$ using properties of logarithms.

Accepted Answer

$$3\log_2$ x + \log_2$ 8 - \log_2$ y$$

Question 5

Condense the expression $$2\log_3$ x - \dfrac{1}{2}\log_3$ y$$ into a single logarithm.

Accepted Answer

$$\log_3$ \left( \dfrac{x^2$}{\sqrt{y}} \right)$$

Question 6

Solve for $$x$$: $$\log_4$ x = 3.$$

Accepted Answer

$$x = 64$$

Question 7

Which of the following statements is TRUE?

Accepted Answer

$$\log_b b = 1$$

Question 8

Rewrite $$\log_2$ 32 as a $$product of an integer and $$\log_2$ 2.$$

Accepted Answer

$$5\log_2$ 2$$

Question 9

If $$\log_7$ x = 2$$, what is the value of $$x$$?

Accepted Answer

$$49$$

Question 10

Which of the following is the correct application of the change of base formula for $$\log_5$ 12$$?

Accepted Answer

$$\dfrac{\log_{10} 12}{\log_{10} 5}$$

Question 11

Evaluate $$\log_3$ 1.$$

Accepted Answer

$$0$$

Question 12

Which of the following is equivalent to $$\log_b (x^k)$$?

Accepted Answer

$$k \log_b x$$

Question 13

A scientist is studying the pH of a solution, which is defined as $$\mathrm{pH} = -\log_{10} [H^+]. If$$ $$[H^+] = 10$$^{-7}$$, what is the pH?

Accepted Answer

$$7$$

Question 14

Solve for $$x$$: $$2^{3x} = 16$.

Accepted Answer

$$x = \dfrac{2}{3}$$

Question 15

Which of the following is the correct expansion of $$\log_5$ \left( \dfrac{25x^2$}{y^3$} \right)$$?

Accepted Answer

$$2\log_5$ x + 2\log_5$ 5 - 3\log_5$ y$$

Question 16

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

Accepted Answer

$$32$$

Question 17

Condense the expression $$\log_4$ x + \log_4$ y - \log_4$ z$$ into a single logarithm.

Accepted Answer

$$\log_4$ \left( \dfrac{xy}{z} \right)$$

Question 18

Solve for $$x$$: $$\log_3$ (x - 2) = 4.$$

Accepted Answer

$$x = 83$$

Question 19

Which of the following is NOT a valid property of logarithms?

Accepted Answer

$$\log_b (x + y) = \log_b x + \log_b y$$

Question 20

A radioactive substance decays according to $$A = A_0$ e$$^{-kt}$$. If A_0$ = 100$$ grams, $$A = 25$$ grams after $$t = 10$$ years, what is the value of $$k$$? (Round to 3 decimal places.)

Accepted Answer

$$k = 0.139$$

C4

Guida di studio - Domande di pratica

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