How do you solve 4 log x= 4?

$x = e$
It's quite simple here, you first divide both sides of the equation by 4, so you now have to solve $\ln \left(x\right) = 1$, which means that $x = e$ because $\ln \left(x\right) = 1 \iff x = {e}^{1} = e$ when you apply the exponential function on both sides of the equation (the exponential is a one-on-one function so it guarantees you the solution you will find is unique).