Find the value of Log 0 for Log function with base 10 and base e on infinitylearn.com. Understand and calculate the value of log 0. So, the value of the expression $~\log_b (0)~$ makes no sense and more specifically, we cannot determine any value for it or we cannot define it. Thus $~\log_b (0)~$ is Indeterminate or Undefined or Does not exist. 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 ... 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: So the base b logarithm of zero is not defined. For example the base 10 logarithm of 0 is not defined: