## 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: