How do you solve 6^x-5=1?

You might just realise $6 - 5 = 1$ and hence conclude $x = 1$.
Or ,you move 5 to the other side to get ${6}^{x} = 6$.
You then take log of both sides $\log {6}^{x} = \log 6$.
$x \log 6 = \log 6$.
$x = \log \frac{6}{\log} 6 = 1$.