Question

If $\frac{3^{2x-8}}{225}=\frac{5^3}{5^x}$, then $x=$

• A. $3$
• B. $5$
• C. $4$
• D. $2$

Answer 1

The correct option is B $5$

Given : $\frac{3^{2x-8}}{225}=\frac{5^3}{5^x}$

$\Rightarrow \frac{3^{2x-8}}{25\times 9}=\frac{5^3}{5^x}$

$\Rightarrow 3^{2x-8}\times 5^x=9\times 5^2\times 5^3$

$\Rightarrow 3^{2x-8}\times 5^x=3^2\times 5^5$

On comparing both sides , we get
$2x-8=2$ and $x=5$
$\Rightarrow x=5$
Hence , (c) is correct answer.