Expand the expression: $$5\text{log}_5 a - 6\text{log}_5 b$$

$$5\text{log}_5 a - 6\text{log}_5 b = \text{log}_5(a^5) - \text{log}_5(b^6) = \text{log}_5\frac{a^5}{b^6}$$ .

Condense the expression: $$\text{log}_8 \frac{6x}{3y}$$

$$\text{log}_8 \frac{6x}{3y} = \text{log}_8(2) + \text{log}_8(x) - \text{log}_8(y)$$ .

Expand the expression: $$4\text{log} u + 16\text{log} v$$

$$4\text{log} u + 16\text{log} v = \text{log}(u^4) + \text{log}(v^{16}) = \text{log}(u^4 v^{16})$$ .

Condense the expression: $$\text{log}_8 a^{18} - \text{log}_8 b^3$$

$$\text{log}_8 \frac{a^{18}}{b^3}$$ .

What is the definition of the base of a logarithm?

The base of a logarithm is the number that is raised to a power to obtain a given number. For example, in $$\text{log}_b(a)$$ , $$b$$ is the base.

What does it mean to condense logarithmic expressions?

To condense logarithmic expressions means to combine multiple logarithmic terms into a single logarithm using properties of logarithms.

What does it mean to expand logarithmic expressions?

To expand logarithmic expressions means to break down a single logarithmic term into multiple terms using properties of logarithms.

What is the relationship between logarithms and exponents?

Logarithms are the inverse operations of exponentiation. If $$b^y = x$$ , then $$\text{log}_b(x) = y$$ .

What is the significance of the logarithm of 1?

The logarithm of 1 in any base is always 0, since any number raised to the power of 0 equals 1: $$\text{log}_b(1) = 0$$ .

Expand and Condense Logarithms Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of a logarithm?

Back

2.

FLASHCARD QUESTION

Front

What is the change of base formula for logarithms?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What is the product property of logarithms?

Back

6.

FLASHCARD QUESTION

Front

What is the quotient property of logarithms?

Back

7.

FLASHCARD QUESTION

Front

What is the power property of logarithms?

Back

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