Question

Solve : $3^{4x+1}-2\times 3^{2x+2}-81=0$

• A. $x=-3$
• B. $x=9$
• C. $x=-1$
• D. $x=1$

Answer 1

Answer: (D)

$x=1$

Given equation is:

$3^{4x+1}-2\times 3^{2x+2}-81=0$

Let $3^{2x}=t$
Hence the equation changes to
$3.t^2-18.t-81=0$
$t^2-6t-27=0$
$t^2-9t+3t-27=0$
$t(t-9)+3(t-9)=0$
$(t+3)(t-9)=0$
$t=-3$ ... not possible.
$\therefore t=9$
$\therefore 3^{2x}=9$
$\therefore 2x=2$
$\therefore x=1$