What is the quotient rule for logarithms?

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

Expand the expression $$\text{log}(3x^2)$$ .

$$\text{log}(3) + 2\text{log}(x)$$ .

What is the power rule for logarithms?

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

Write the equation of the logarithm after applying the transformations: Shifted up 30, reflected over the x-axis, to the right by 5 from $$\text{ln}(x)$$ .

$$f(x) = -\text{ln}(x-5) + 30$$ .

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

$$3$$ , because $$10^3 = 1000$$ .

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 produce a given number. For example, in $$\text{log}_b(x)$$ , $$b$$ is the base.

A3 Final Rev Units 8, 9 (Exponentials and Logs) Flashcards

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1.

FLASHCARD QUESTION

Front

What is the definition of a logarithm?

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2.

FLASHCARD QUESTION

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What is the relationship between logarithms and exponents?

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3.

FLASHCARD QUESTION

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Back

4.

FLASHCARD QUESTION

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5.

FLASHCARD QUESTION

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What is the formula for changing the base of a logarithm?

Back

6.

FLASHCARD QUESTION

Front

What is the natural logarithm?

Back

7.

FLASHCARD QUESTION

Front

What is the product rule for logarithms?

Back

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