Alright, so the idea of an exponent, $x$, is that you are multiplying its base by itself $x$ number of times. With base $5$ and $x=3$, we have that $5^3$ = $5 \cdot 5 \cdot 5$
I understand that the logarithm with base $a$ of $x = c$,
tells us that
$$a^c = x$$
and for $c =$ positive; values for $x$ are greater than $1$,
and for $c =$ negative; values for $x$ are less than $1$,
and for $c = 0$, values for $x$ are...$1$.
So in short, I understand how, by means of observation of the graph of $f(x) = \log x$, we can see that $f(1) = 0$, BUT, I see no other way to understand why $x^0 = 1$, apart from the graph and everything around that very point.
I honestly cannot get my head around the idea, "$5$ times itself $0$ times... is one".
Is it that there is no fundamental answer for this but that we simply know by the graph? Or can I truly understand $x^0 = 1$ on its own?