If 125^x=25/5 ^xfind x.

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Solution

125^x=25/5 ^x

⇒ (5³)^x= 5²/5 ^x

⇒ 5^3x= 5^2-x

⇒ 3x = 2-x

⇒ 4x = 2

⇒ x = 2/4

⇒ x = 1/2 Ans.

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5 x - 4 y = 7

x y = 8

125 x^{3} - 64 y^{3}

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\frac{x^{2} - 5 x + 12}{5 x - 12} = \frac{x^{2} - x - 4}{x + 4}

(125 x^{- 3})^{\frac{1}{3}}

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

5 x + \frac{1}{5 x} = 23

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

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

{log}_{x} (125 x) \cdot {log}_{25}^{2} x = 1

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