Find the value of $x$ if $5^{x} + 5^{x - 1} = 750$

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Solution

$\begin{matrix} W e h a v e 5^{x} + 5^{x - 1} = 750 5^{x} (1 + \frac{1}{5}) = 750 5^{x} (\frac{6}{5}) = 750 5^{x} = \frac{750 \times 5}{6} 5^{x} = 125 \times 5 5^{x} = 5^{4} ∴ x = 4 H e n c e, t h e v a l u e o f x i s 4. \end{matrix}$

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