Find the value of $x$ if $5^{x} + 5^{x + 1} + 5^{x + 2} = 775$

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Solution

$\begin{matrix} W e h a v e 5^{x} + 5^{x + 1} + 5^{x + 2} = 775 \Rightarrow 5^{x} [1 + 5^{1} + 5^{2}] = 775 \Rightarrow 5^{x} [31] = 775 \Rightarrow 5^{x} = \frac{775}{31} \Rightarrow 5^{x} = 25 \Rightarrow 5^{x} = 5^{2} ∴ x = 2 h e n c e, t h e v a l u e o f x i s 2. \end{matrix}$

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