Question

If log 3 to the base x-1 is 3,then,find x.​

Answer 1

$\tt {log}_{x-1}{3} = 2 \\ \\ \tt We\:know\:that \\ \\ \tt \boxed{\bold{\underline{\green {\tt {log}_{b}{a} = x {b}^{x} = a }}}}}\\ \\ \tt \implies {(x-1)}^{2} = 3 \\ \\ \tt \implies x -1 = \sqrt{3}\\ \\ \tt \implies x = \sqrt{3}+1 \\ \\ \tt \therefore \boxed{\bold{\underline{\red{ \tt x = 1+ \sqrt{3} }}}}}$