I am watching a logarithm lecture from 3Blue1Brown (great for math dummies like me!) Here is the video for context: https://youtu.be/4PDoT7jtxmw?t=1306
The step that I did not follow is when he equates the LHS and RHS of the equation below. Maybe someone can fill me in on the general rule that allows us to claim this equality? thanks in advance !
$\log _{10}(e)=\left[\log _e(10)\right]^{-1}$
It's probably based on the base change formula that is well-known:
$ \operatorname{log}_b{a} = \frac{\operatorname{log}{b}}{\operatorname{log}{a}} $
From this, raising to -1 power means flipping the fraction
$ \operatorname{log}_b{a} = \frac{\operatorname{log}{b}}{\operatorname{log}{a}} = \bigl[\frac{\operatorname{log}{a}}{\operatorname{log}{b}}\bigr]^{-1} = \bigl[\operatorname{log}_a{b}\bigr]^{-1} $