log base 10 x = logx

The natural logarithm is the logarithm having base e, where

The common logarithm is the logarithm to base 10.

You can probably find both definitions in wikipedia.

The value of the common logarithm is undefined at 0.

The common logarithm (base 10) of 2346 is 3.37. The natural logarithm (base e) is 7.76.

A logarithm is the exponent to which a number called a base is raised to become a different specific number. A common logarithm uses 10 as the base and a natural logarithm uses the number e (approximately 2.71828) as the base.