The logarithm, like multiplication and exponentiation, is a mathematical operation. Here is an example:

log₂16

This statement reads "log base 2 of 16." "log" is short for logarithm, and 2 is called the base.

Logarithms are inverse operations of exponentiation. For example:

2⁴ = 16

and

log₂16 = 4

Here are some more examples:

• log₂ of 8 = 3
• log₃ of 9 = 2
• log₄ of 256 = 4

In general,

if x^p = z, then log_xz = p

Conversely,

if log_xz = p, then x^p = z

Raising a number to a positive power increases the number, whereas a logarithm of a positive number decreases the number.