Question

If $(9{)}^{x+2}=240+9^x$, then $x=$

• A. $0.2$
• B. $0.1$
• C. $0.4$
• D. $0.5$

Answer 1

The correct option is D $0.5$

Given : $(9{)}^{x+2}=240+9^x$
$\Rightarrow 9^x{.9}^2=240+9^x$
$\Rightarrow 9^x.81-9^x=240$
$\Rightarrow (81-1)\times 9^x=240$
$\Rightarrow 9^x=\frac{240}{80}=3$
$\Rightarrow (3^2{)}^x=3$
$\Rightarrow 3^{2x}=3^1$
On comparing both the sides , we get
$2x=1$
$x=\frac{1}{2}=0.5$
Hence, option (a) is correct.