Logarithmic Functions

Front

What is a logarithmic function?

Back

A logarithmic function is the inverse of an exponential function, expressed as y = log_b(x), where b is the base and x is the argument.

Front

What is the base of a logarithm?

Back

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

Tags

CCSS.HSF.BF.B.5

Front

Calculate: log_5(25) = ?

Back

2

Front

What is the range of logarithmic functions?

Back

The range of logarithmic functions is all real numbers.

Tags

CCSS.HSF-IF.C.7E

Front

What is the domain of logarithmic functions?

Back

The domain of logarithmic functions is x > 0.

Front

What is a vertical asymptote in logarithmic functions?

Back

A vertical asymptote in logarithmic functions occurs at x = 0.

Tags

CCSS.HSF-IF.C.7E

Front

What is a horizontal asymptote in exponential functions?

Back

A horizontal asymptote in exponential functions occurs at y = 0.

Tags

CCSS.HSF-IF.C.7D

Front

What is the relationship between logarithmic and exponential functions?

Back

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

Tags

CCSS.HSF.BF.B.5

Front

What is the value of log_10(1000)?

Back

3

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.