PH: L3.2 Logarithmic Functions and Their Graphs

Front

What is a logarithm?

Back

A logarithm is the power to which a number must be raised to obtain another number. For example, if b^y = x, then log_b(x) = y.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power. In log_b(x), b is the base.

Front

What is the relationship between exponential and logarithmic functions?

Back

Logarithmic functions are the inverses of exponential functions. If y = b^x, then x = log_b(y).

Front

What is the logarithmic identity log_b(b) = ?

Back

log_b(b) = 1, because any number raised to the power of 1 is itself.

Front

What is the logarithmic identity log_b(1) = ?

Back

log_b(1) = 0, because any number raised to the power of 0 is 1.

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

How do you graph a logarithmic function?

Back

To graph a logarithmic function, plot points by calculating values for x and y, noting that the graph passes through (1,0) and approaches the vertical line x=0.

Front

What is the domain of a logarithmic function?

Back

The domain of a logarithmic function is (0, ∞), meaning it only accepts positive real numbers.

Front

What is the range of a logarithmic function?

Back

The range of a logarithmic function is (-∞, ∞), meaning it can take any real number as a value.

Front

What does the graph of a logarithmic function look like?

Back

The graph of a logarithmic function is a curve that increases slowly and approaches the vertical axis but never touches it.