General Logarithm/Examples/Base b of -1

Theorem
Let $b \in \R_{>0}$ be a strictly positive real number such that $b \ne 1$.

Let $\log_b$ denote the logarithm to base $b$.

Then:
 * $\log_b \left({-1}\right)$ is undefined in the real number line.

Proof
$\log_b \left({-1}\right) = y \in \R$.

Then:
 * $b^y = -1 < 0$

But from Power of Positive Real Number is Positive:
 * $b^y > 0$

The result follows by Proof by Contradiction.