## Logarithm of Zero

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

The real logarithmic function log

(x) is defined only for x>0._{b}We can't find a number x, so the base b raised to the power of x is equal to zero:

b= 0 ,^{ x}xdoes not existSo the base b logarithm of zero is not defined.

log

(0) is not defined_{b}For example the base 10 logarithm of 0 is not defined:

log

_{10}(0) is not definedThe limit of the base b logarithm of x, when x approaches zero from the positive side (0+), is minus infinity:

## See also