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Exponential Representation for Irrational Numbers

If 5 x + 5 ...

Question

If $5^{x} + 5^{x} + 5^{x} + 5^{x} + 5^{x} = 625$ Find $x$ .

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Solution

$5^{x} + 5^{x} + 5^{x} + 5^{x} + 5^{x} = 625$
$⟹ 5 \times 5^{x} = 5^{4}$
$⟹ 5^{x + 1} = 5^{4}$
$⟹ x + 1 = 4$
$⟹ x = 3$

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l o g 4 {(\sqrt{5})}^{x} = 625

5^{x} + 5^{x} + 5^{x} + 5^{x} + 5^{x} = 5

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5 x - \frac{1}{5 x} = 17

25 x^{2} - \frac{1}{25} x^{2}

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