A logarithm is the exponent 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 an exponential function?

An exponential function is a mathematical function of the form $$f(x) = a \times b^x$$ , where $$a$$ is a constant, $$b$$ is the base, and $$x$$ is the exponent.

What is the relationship between logarithmic and exponential functions?

Logarithmic functions are the inverses of exponential functions. If $$y = b^x$$ , then $$x = \text{log}_b(y)$$ .

What is the base of a logarithm?

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

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

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

What does it mean if $$\text{log}_b(a) = 0$$ ?

If $$\text{log}_b(a) = 0$$ , it means that $$a = 1$$ , since any base raised to the power of 0 equals 1.

Evaluating Logarithmic and Exponential Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Define a logarithm.

Back

2.

FLASHCARD QUESTION

Front

What is the change of base formula for logarithms?

Back

3.

FLASHCARD QUESTION

Front

Solve for x: log₅(x) - log₅(2) = log₅(15)

Back

x = 30.

4.

FLASHCARD QUESTION

Front

What is the product property of logarithms?

Back

5.

FLASHCARD QUESTION

Front

What is the quotient property of logarithms?

Back

6.

FLASHCARD QUESTION

Front

What is the power property of logarithms?

Back

7.

FLASHCARD QUESTION

Front

Solve for x: log₄(3x-1) = log₄(2x+3)

Back

x = 4.

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