Question

Solve the following quadratic equations by factorization method :
$3^{2x}-3\times 10\times 3^x+81=0$

Answer 1

$3^{2x}-3\times 10\times 3^x+81=0$

$⟹3^{2x}-3^{x+1}\times 10+3^4=0$

$⟹(3^x{)}^2-30\times (3^x)+81=0$

Let, $3^x=u$

$⟹u^2-30u+81=0$

$⟹u^2-27u-3u+81=0$

$⟹u(u-27)-3(u-27)=0$

$⟹(u-3)(u-27)=0$

When, $u=3$

$⟹x=1$

And when, $u=27$

$⟹x=3$