Question 1

Express $$\log_6$ 216 = 3 in $$exponential form.

Accepted Answer

$$6^3 = 216$

Question 2

Which of the following is the correct logarithmic form of $$8^{-\frac{2}$${3}} = \frac{1}{4}$$?

Accepted Answer

$$\log_8$ \frac{1}{4} = -\frac{2}{3}$$

Question 3

Evaluate $$\log_5$ 125$$ without a calculator.

Accepted Answer

$$3$$

Question 4

Which of the following is the correct exponential form of $$\log_{\frac{1}{2}} 32 = -5$$?

Accepted Answer

$$\left(\frac{1}{2}\$$right)^{-5}$$ = 32$$

Question 5

Evaluate $$\log_3$ \frac{1}{9}$$ without a calculator.

Accepted Answer

$$-2$$

Question 6

If $$\log_{64} 8 = x$$, what is the value of $$x$$?

Accepted Answer

$$\frac{1}{2}$$

Question 7

Evaluate $$\log_{25} 5$$ without a calculator.

Accepted Answer

$$\frac{1}{2}$$

Question 8

A road construction crew is blasting through a mountain side. If the intensity of the blast is $$1.65 	imes 10$$^{-2}$$ W/m^2$, what is the decibel level D$? Use D = 10$$ \log_{10} \left( \frac{I}{$$I_0$$} ight)$$, where I_0$ = 10$$^{-12}$$ W/m^2$. Round to the nearest integer.

Accepted Answer

$$112 dB$$

Question 9

The amount of energy released from one earthquake was 8,000 times greater than another. The equation $$10^x = 8000$$ represents this situation. To the nearest thousandth, what is $$x$$?

Accepted Answer

$$3.903$$

Question 10

Find the magnitude $$R of an $$earthquake where $$a = 325$$, $$T = 4$$, and $$B = 3.25$$ using $$R = \log_{10} \left( \frac{a}{T} \right) + B.$$

Accepted Answer

$$4.36$$

Question 11

Venus and Jupiter have magnitudes $$m_1 = -4.3$ and m_2$ = -2.1$$ respectively. Using $$m_2$$ - $$m_1 = -2.5$$ \log_{10} \left( \frac{$$b_2$$}{$$b_1$$} \right)$$, how many times brighter is Venus than Jupiter?

Accepted Answer

$$8.32$$

Question 12

Evaluate $$\log_3$ 81$$ without a calculator.

Accepted Answer

$$4$$

Question 13

Which of the following is the correct logarithmic form of $$10^{-3} = 0.001$?

Accepted Answer

$$\log_{10} 0.001 = -3$$

Question 14

Evaluate $$4^{\log_4 6}$$ without a calculator.

Accepted Answer

$$6$$

Question 15

If $$\log_\pi 57 is $$evaluated using a calculator, which value is closest to the result?

Accepted Answer

$$2.857$$

Question 16

The intensity levels $$L of $$two earthquakes can be compared by $$\log_{10} \left( \frac{I_1$}{I_2$} \right) = M_1$ - M_2$. If M_1$ = 9.0$$ and $$M_2 = 6.1$, how many times greater was the intensity of the 2011 earthquake compared to the 2009 earthquake? Round to the nearest hundredth.

Accepted Answer

$$794.33$$

Question 17

Evaluate $$\log_3$ \frac{1}{27}$$ without a calculator.

Accepted Answer

$$-3$$

Question 18

Which of the following is the correct exponential form of $$\log_4$ 8 = x$$?

Accepted Answer

$$4^x = 8$$

Question 19

If $$\log_7$ x = 0.845$$, what is $$x in $$exponential form?

Accepted Answer

$$x = 7$$^{0.845}$$

Logarithmic Expressions and Applications – Precalculus Study Guidance

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