Question

The value of $x$ such that $3^{2x}-2\left(3^{x+2}\right)+81=0$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$
• E. $5$

Answer 1

The correct option is B $2$

Given equation is $3^{2x}-2\left(3^{x+2}\right)+81=0$

$\Rightarrow 3^{2x}-{2.3}^x{.3}^2+81=0$

$\Rightarrow 3^{2x}-{18.3}^x+81=0$

Let $3^x=t$

Therefore,

$t^2-18t+81=0$

$\Rightarrow t^2-9t-9t+81=0$

$\Rightarrow t(t-9)-9(t-9)=0$

$\Rightarrow (t-9{)}^2=0$

$\Rightarrow t=9$

On re-substituting the value, we get

$3^x=9$

$\Rightarrow 3^x=3^2$

$\Rightarrow x=2$