Choose the correct answer form the alternatives given.
If $5^{x + 3} = (25)^{3 x - 4},$ then what is the value of x?

\frac{5}{11}

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\frac{11}{3}

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\frac{11}{5}

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\frac{13}{5}

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Solution

The correct option is C $\frac{11}{5}$
$5^{x + 3} = (25)^{3 x - 4}$
On comparing, we get
$\Rightarrow$ $x + 3 = 2 (3 x - 4)$ $\Rightarrow$ $5 x = 3 + 8$
Hence, $x = \frac{11}{5}$

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