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.

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.

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.

Front

What is a horizontal asymptote in exponential functions?

Back

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

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).

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.