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Product Law

If 5x+3=253...

Question

If $5^{x + 3} = 25^{3 x - 4}$ , then find $x$ .

\frac{11}{5}

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\frac{5}{6}

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\frac{3}{5}

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\frac{7}{5}

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Solution

The correct option is A $\frac{11}{5}$
$5^{x + 3} = 25^{3 x - 4}$
$\Rightarrow 5^{x + 3} = (5^{2})^{3 x - 4}$
$\Rightarrow 5^{x + 3} = 5^{6 x - 8}$
$\Rightarrow x + 3 = 6 x - 8$
$\Rightarrow 5 x = 11$
$\Rightarrow x = \frac{11}{5}$

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