# Logarithm of Zero

What is the logarithm of zero? Why log(0) is not defined.

The real logarithmic function log_{b}(x) is defined only for x>0.

We can't find a number x, so the base b raised to the power of x
is equal to zero:

*b*^{ x} = 0 , *x* does not exist

So the base b logarithm of zero is not defined.

log_{b}(0) is not defined

For example the base 10 logarithm of 0 is not defined:

log_{10}(0) is not defined

The limit of the base b logarithm of x, when x approaches zero from the
positive side (0+), is
minus infinity:

Logarithm of one
►

## See also