Question

Solve the following quadratic equations by factorization method :
$9^x-12\times 3^x+27=0$

Answer 1

$9^x-12\times 3^x+27=0$

$⟹(3^2{)}^x-12\times (3^x)+27=0$

Let, $3^x=u$

$⟹u^2-12u+27=0$

$⟹u^2-9u-3u+27=0$

$⟹u(u-9)-3(u-9)=0$

$⟹(u-3)(u-9)=0$

When, $u=3$

$⟹x=1$

And when, $u=9$

$⟹x=2$