Why value of log0 is undefined?

Answer 1

Let's assume a base 10, although the following reasoning works for any other base as well (e.g., for natural logarithms, base e) .

x = log10100

is defined as the solution of:

10x = 100

And the solution is 2. On the other hand,

x = log100

is the solution of:

10x = 0

This has no solution, as you can easily verify. If the exponent, x, gets smaller and smaller (tending towards minus infinity), the expression gets closer and closer to zero, but never quite reaches it.