Solve-for-x-in-the-equation-625-x-5-200-x-3-

Question Number 11263 by tawa last updated on 18/Mar/17

Solve for x in the equation .

625^{x - 5} = 200 \sqrt{x^{3}}

Answered by ajfour last updated on 18/Mar/17

5^{4 (x - 5)} = {200 x}^{3 / 2}

5^{4 x - 20} = 5^{2} {(4 x)}^{3 / 2}

5^{4 x - 22} = {(4 x)}^{3 / 2}

5^{4 x} {(4 x)}^{- 3 / 2} = 5^{22}

clearly if 4 x = 25

5^{25} {(5)}^{- 3} = 5^{22}

Hence 4 x = 25

x = \frac{25}{4}

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