Evaluate $$\text{log}_2(8)$$ .

$$\text{log}_2(8) = 3$$ because $$2^3 = 8$$ .

Evaluate $$\text{log}_3(27)$$ .

$$\text{log}_3(27) = 3$$ because $$3^3 = 27$$ .

What is the product rule for logarithms?

The product rule states that $$\text{log}_b(m \times n) = \text{log}_b(m) + \text{log}_b(n)$$ .

What is the quotient rule for logarithms?

The quotient rule states that $$\text{log}_bigg(\frac{m}{n}igg) = \text{log}_b(m) - \text{log}_b(n)$$ .

What is the power rule for logarithms?

The power rule states that $$\text{log}_b(m^p) = p \times \text{log}_b(m)$$ .

Convert $$\text{log}_5(25) = 2$$ to exponential form.

The exponential form is $$5^2 = 25$$ .

What is the value of $$\text{log}_{10}(1000)$$ ?

$$\text{log}_{10}(1000) = 3$$ because $$10^3 = 1000$$ .

If $$\text{log}_b(1) = 0$$ , explain why this is true.

This is true because any base raised to the power of 0 equals 1, i.e., $$b^0 = 1$$ .

Logarithms Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of a logarithm?

Back

Tags

CCSS.HSF.BF.B.5

2.

FLASHCARD QUESTION

Front

Convert the logarithmic equation log_b(x) = y to exponential form.

Back

Tags

CCSS.HSF.BF.B.5

3.

FLASHCARD QUESTION

Front

What is the base of a common logarithm?

Back

The base of a common logarithm is 10.

4.

FLASHCARD QUESTION

Front

What is the base of a natural logarithm?

Back

The base of a natural logarithm is the constant e (approximately 2.718).

Tags

CCSS.HSF.BF.B.5

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.BF.B.5

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.BF.B.5

7.

FLASHCARD QUESTION

Front

What is the change of base formula for logarithms?

Back

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