if a raised to the nth power is equal to x (a>0, and a is not equal to 1), then the number n is called the logarithm (logarithm) of x with a as the base, recorded as n=logax. among them, a is called the base of the logarithm, x is called the real number, and n is called the "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 base of the irrational number e (e=2.71828...) is called the natural logarithm (natural logarithm) and is recorded as ln.

zero has no logarithm.