Definition of Logarithm

Front

What is a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another number. It is the inverse operation of exponentiation.

Front

Write the logarithmic form of the equation: 2^(-4) = 1/16.

Back

log_2(1/16) = -4

Front

Change to exponential form: log_6(36) = 2.

Back

6^2 = 36

Front

Rewrite log_2(8) = 3 in exponential form.

Back

2^3 = 8

Front

Write the logarithmic form of the equation: 2^x = y.

Back

log_2(y) = x

Front

Write in logarithmic form: y = 10^x.

Back

log(y) = x

Front

What is the base of a logarithm?

Back

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

Front

If log_b(a) = c, what is the equivalent exponential form?

Back

b^c = a

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

What is the logarithm of 1 in any base?

Back

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