Question

If
${5}^{x} - {5}^{x - 1} = 100$
then find the value of x...

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Answer 1

Answer:

x = 3

Explanation:

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Answer 2

Explanation:

$\implies{{5}^{x} - {5}^{x - 1} = 100} \\ </p><p> \implies{{5}^{x} - \frac{ {5}^{x} }{5} = 100} \\</p><p> \implies{{5}^{x} (1 - \frac{1}{5} ) = 100} \\ </p><p> \implies{{5}^{x} ( \frac{5 - 1}{5} ) = 100} \\ </p><p> \implies{{5}^{x} \times \frac{4}{5} = 100} \\ </p><p> \implies{{5}^{x} = 100 \times \frac{5}{4}} \\ </p><p> \implies{{5}^{x} = 25 \times 5 \\ {5}^{x} = 125} \\ </p><p> \implies{{5}^{x} = {5}^{3}} \\ \\</p><p> \blue{Since \: base \: are \: same \: so \: we \: equate \: the \: power.} \\ \\ </p><p>so \: \\ </p><p>\implies{x =3} \\ \\ \\ </p><p>$

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