Question

Solve the following equation:
${\log }_{x-1}3=2$

Answer 1

${log}_{x-1}3=2\Rightarrow 3=({x-1)}^2\Rightarrow x^2-2x-2=0\Rightarrow x=\frac{2\pm \sqrt{4+8}}{2}\Rightarrow x=\frac{2\pm 2\sqrt{3}}{2}\Rightarrow x=1+\sqrt{3}(\because x\ne 1-\sqrt{3})$