Question

Solve the following equations:
$3^{2x}+9={10.3}^x$.

• A. $-2,0$
• B. $2,0$
• C. $2,1$
• D. $2,3$

Answer 1

The correct option is B $2,0$

Given, $3^{2x}+9=10.3^x$

${\left(3^x\right)}^2+9=10.3^x$

Put $3^x=t$

Therefore, $t^2+9=10t$

$\Rightarrow t^2-10t+9=0$

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

$\Rightarrow (t-1)(t-9)=0$

$\Rightarrow t=1,9$

Resubtituting values, we get

$3^x=1$

$\Rightarrow 3^x=3^0$

$\Rightarrow x=0$

and $3^x=9$

$\Rightarrow 3^x=3^2$

$\Rightarrow x=2$

Thus, the values of $x$ are $0,2$.