If a raised to the power of n is equal to x (a>0, and a is not equal to 1), then the number n is called the logarithm of x with a as the base, and is written as n=logax. Among them, a is called the base of the logarithm, x is called a real number, and n is called "logarithm of x with a as the base".

In particular, we call the base 10 logarithm the common logarithm, and we write it as lg.

The logarithm with the irrational number e (e=2.71828...) as the base is called the natural logarithm and is denoted by ln.

Zero has no logarithm.