Question

Find the value of $x$ from $2{\log }_3(x-1)=4$

Answer 1

$2{\log }_3(x-1)=4=4{\log }_{3}3$

$\Rightarrow {\log }_3(x-1{)}^2={\log }_3{3}^4$

$\Rightarrow (x-1{)}^2=3^4\Rightarrow (x-1{)}^2-(3^2{)}^2=0$

$\Rightarrow (x-1-3^2)(x-1+3^2)=0\Rightarrow (x-10)(x+8)=0$

$\Rightarrow x=10$ and $x=-8$ (Not possible because ${\log }_3(x-1)$ will be invalid.)

Hence, $x=10$