Question

$\log 8=\log (x-1)-\log 20$. solve for $x$?

Answer 1

$x=161$

Given : $\log \left(8\right)=\log (x-1)-\log \left(20\right)$

Add $\log \left(20\right)$ to both sides and flip the equation :

$\log (x-1)=\log \left(8\right)+\log \left(20\right)$

Addition implies multiplication within the argument:

$\log (x-1)=\log (8\times 20)$

$\log (x-1)=\log \left(160\right)$

The argument must be equal :

$x-1=160$

Add one to both sides :

$x=161$