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

$$\mathrm{Solve}\mathrm{for}\mathrm{x}\mathrm{in}\mathrm{the}\mathrm{equation}.$$$${625}^{\mathrm{x}-5}=200\sqrt{{\mathrm{x}}^3}$$

Answered by ajfour last updated on 18/Mar/17

$$5^{4(\mathrm{x}-5)}={200\mathrm{x}}^{3/2}$$$$5^{4\mathrm{x}-20}=5^2{\left(4\mathrm{x}\right)}^{3/2}$$$$5^{4\mathrm{x}-22}={\left(4\mathrm{x}\right)}^{3/2}$$$$5^{4\mathrm{x}}{\left(4\mathrm{x}\right)}^{-3/2}=5^{22}$$$$\mathrm{clearly}\mathrm{if}4\mathrm{x}=25$$$$5^{25}{\left(5\right)}^{-3}=5^{22}$$$$\mathrm{Hence}4\mathrm{x}=25$$$$\mathrm{x}=\frac{25}{4}$$

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