$$\log(a \times b) = \log(a) + \log(b)$$

Question 1

Which of the following correctly expands $$\log\left(\frac{x^a}{y^b}\right)$$ using the laws of logarithms?

Accepted Answer

$$a\log(x) - b\log(y)$$

Question 2

Given $$\log(375) = 2.574$$, what is the value of $$\log(3.75)$$?

Accepted Answer

$$1.574$$

Question 3

If $$\log(57.3) = 1.758$$, what is $$\log(0.573)$$?

Accepted Answer

$$-0.242$$

Question 4

Which law of exponents corresponds to the logarithmic law $$\log(ab) = \log(a) + \log(b)$$?

Accepted Answer

$$a^m \cdot a^n = a$$^{m+n}$$

Question 5

Solve for $$x in $$the equation $$10^{3x}$$ 	imes 2 = 7$$.

Accepted Answer

Question 6

Given $$\log(352) = 2.546$$ and $$\log(17.7) = 1.248$$, use logarithms to compute $$352 	imes 17.7.$$

Accepted Answer

$$6,230.4$$

Question 7

If $$\log(2.7) = 0.431$$ and $$\log(1.6) = 0.204$$, use logarithms to compute $$2.7 	imes 1.6.$$

Accepted Answer

Question 8

If $$\log(38.2) = 1.582$$ and $$\log(1.77) = 0.248$$, use logarithms to compute $$38.2 \div 1.77.$$

Accepted Answer

$$21.6$$

Question 9

Which of the following is the correct definition of the antilogarithm of a number $$y$$?

Accepted Answer

$$10^y$$

Question 10

If $$\log(x) = 2.306$$, what is the value of $$x$$?

Accepted Answer

$$10^{2.306}$$

Question 11

A chemist needs to multiply two concentrations: $$0.573$$ and $$57.3. $$Using logarithms, what is the result?

Accepted Answer

$$32.84$$

Question 12

Which logarithmic law allows you to write $$\log(a^n) as$$ $$n\log(a)$$?

Accepted Answer

$$\log(a^n) = n\log(a)$$

Question 13

A medical researcher needs to divide two values: $$38.2$$ and $$1.77. $$Using logarithms, what is the result?

Accepted Answer

$$21.6$$

Question 14

If $$\log(3.86) = 0.587$$, what is the antilogarithm of $$3.86$$?

Accepted Answer

$$10^{3.86}$$

Question 15

Which of the following is NOT a law of logarithms?

Accepted Answer

$$\log(a + b) = \log(a) + \log(b)$$

Question 16

A historian is analyzing population growth. If the population increases from $$1,000 to$$ $$10,000$$, what is $$\log(10,000) - \log(1,000)$$?

Accepted Answer

$$1$$

Question 17

If $$\log(2) = 0.301$$ and $$\log(5) = 0.699$$, what is $$\log(10)$$?

Accepted Answer

$$1$$

Question 18

Which of the following is the correct way to use logarithms to multiply $$a$$ and $$b$$?

Accepted Answer

$$\log(a 	imes b) = \log(a) + \log(b)$$

Question 19

A biologist needs to expand $$\log\left(\frac{a^3$b^2$$}{$$c^4$$}\right)$ as much as possible. Which is correct?

Accepted Answer

$$3\log(a) + 2\log(b) - 4\log(c)$$

Lecture 11: Logarithms: Properties, Computation, and Applications

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