Expand the expression: $$\text{log}_2(16)$$

$$\text{log}_2(4) + \text{log}_2(4)$$ or $$\text{log}_2(2^4) = 4$$ .

Expand the expression: $$\text{log}_4(6y)$$

$$\text{log}_4(6) + \text{log}_4(y)$$ .

What is 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.

Expand the expression: $$\text{log}_4(3xy)$$

$$\text{log}_4(3) + \text{log}_4(x) + \text{log}_4(y)$$ .

What is the change of base formula for logarithms?

The change of base formula allows you to convert a logarithm to a different base: $$\text{log}_b(a) = \frac{\text{log}_k(a)}{\text{log}_k(b)}$$ for any base k.

What is the value of $$\text{log}_b(b)$$ ?

The value of $$\text{log}_b(b) = 1$$ because any number raised to the power of 1 is itself.

What is the value of $$\text{log}_b(1)$$ ?

The value of $$\text{log}_b(1) = 0$$ because any number raised to the power of 0 is 1.

What is the relationship between logarithms and exponents?

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

Properties of Logs - Product Rule Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Product Rule of Logarithms?

Back

2.

FLASHCARD QUESTION

Front

Condense the expression: log₅3 + log₅6 + log₅9

Back

log₅162

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What does it mean to expand a logarithm?

Back

Expanding a logarithm involves breaking it down into a sum of simpler logarithmic expressions using the Product Rule or Quotient Rule.

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the Quotient Rule of Logarithms?

Back

7.

FLASHCARD QUESTION

Front

Back

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