8.9 Graphing Logarithmic Functions

Front

What is the base of a logarithmic function?

Back

The base of a logarithmic function is the number that is raised to a power to obtain a given value. For example, in log_b(x), b is the base.

Front

Logarithmic functions are the inverse of which type of functions?

Back

Logarithmic functions are the inverse of exponential functions.

Front

How are exponential functions and logarithmic functions related?

Back

Exponential functions and logarithmic functions are inverses of each other.

Front

What is the range of the function log(x)?

Back

The range of log(x) is (-∞, ∞).

Front

What is the domain of the function log(x)?

Back

The domain of log(x) is (0, ∞).

Front

What does log_b(x) represent?

Back

log_b(x) represents the logarithm of x to the base b, which answers the question: 'To what power must b be raised to obtain x?'

Front

What is the value of log_5(25)?

Back

The value of log_5(25) is 2, because 5^2 = 25.

Front

What is the value of log_10(1000)?

Back

The value of log_10(1000) is 3, because 10^3 = 1000.

Front

What is the change of base formula for logarithms?

Back

The change of base formula is log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(xy) = log_b(x) + log_b(y).