Is there proof show that $\log x$ is undefined and make no sense at $ x=0$? I was asked by someone: why $\log x$ is undefined at $x=0 $?
Is there proof  show that $\log x$ is undefined at $x=0$?
Note(01):: log is the inverse function of the exponential function.
note(02): I edited my question as I meant why it's not make a sens at $x=0$ ?
Thank you for your help .

For the exponential function we all agree that $exp(- \infty) = 0$. Now the logarithm is the inverse of the exponential function. Applying it to both sides we obtain: $log(0) = - \infty$. This is perfectly sound, but mathematicians prefer to exclude the point $x = 0$ from the domain. That is all, really.  
