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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 (logarithm), denoted by 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 logarithm with base 10 the common logarithm, and record it as lg.

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

Zero has no logarithm.