A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to produce a given number. For example, if $$b^y = x$$ , then $$\text{log}_b(x) = y$$ .

What is the inverse of $$f(x) = 6^x$$ ?

The inverse is $$f^{-1}(x) = \text{log}_6(x)$$ .

Evaluate $$\text{log}_7\frac{1}{49}$$ .

$$\text{log}_7\frac{1}{49} = -2$$ because $$7^{-2} = \frac{1}{49}$$ .

Evaluate $$\text{log}_8\frac{1}{8}$$ .

$$\text{log}_8\frac{1}{8} = -1$$ because $$8^{-1} = \frac{1}{8}$$ .

What is the change of base formula for logarithms?

The change of base formula states that $$\text{log}_b(a) = \frac{\text{log}_k(a)}{\text{log}_k(b)}$$ for any base $$k$$ .

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 $$\text{log}_b\frac{m}{n} = \text{log}_b(m) - \text{log}_b(n)$$ .

What is the power rule for logarithms?

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

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

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

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

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

Graphing Log Functions with review Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a logarithm?

Back

2.

FLASHCARD QUESTION

Front

What is the base of a logarithm?

Back

3.

FLASHCARD QUESTION

Front

What is the relationship between logarithms and exponents?

Back

4.

FLASHCARD QUESTION

Front

What is the horizontal asymptote of a logarithmic function?

Back

5.

FLASHCARD QUESTION

Front

What is the horizontal asymptote of an exponential function?

Back

6.

FLASHCARD QUESTION

Front

How do you find the inverse of a function?

Back

To find the inverse of a function, swap the x and y variables and solve for y.

7.

FLASHCARD QUESTION

Front

Back

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