$5^{x - 3} \times 3^{2 x - 8} = 225$

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Solution

We have,

$5^{x - 3} \times 3^{2 x - 8} = 225$

$\frac{5^{x}}{5^{3}} \times \frac{3^{2 x}}{3^{8}} = 225$

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

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

$5^{x} \times 3^{2 x} = 5^{5} \times 3^{10}$

$5^{x} \times 3^{2 x} = 5^{5} \times 3^{2 \times 5}$

So, $x = 5$

Hence, the value of $x$ is $5$ .

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