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Given: \(5*\sqrt[x]{125}=\frac{1}{5^{\frac{1}{x}}}\) We get: 5^(3/x + 1) = 5^(-1/x) Since the bases are equal, we can conclude: 3/x + 1 = -1/x Multiply both sides by x to get: 3 + x = -1 Solve: x = -4

Re: If 5*125^(1/x) = 1/(5^(1/x)), then x = ?
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17 Jul 2017, 05:27

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If \(5*\sqrt[x]{125}=\frac{1}{5^{\frac{1}{x}}}\), then x = ?

\(5*\sqrt[x]{125}=\frac{1}{5^{\frac{1}{x}}}\)

\(5 * (125)^{\frac{1}{x}} = 5^{\frac{-1}{x}}\)

\(5^1 * (5)^{\frac{3}{x}} = 5^{\frac{-1}{x}}\)

\((5)^{{1} + \frac{3}{x}} = 5^{\frac{-1}{x}}\)

\({{1} + \frac{3}{x}} = {\frac{-1}{x}}\)

\(\frac{(x + 3)}{x} = \frac{-1}{x}\)

\(x + 3 = -1\)

\(x = -4\)

Hence, Answer is A

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