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Question Number 19194 by mondodotto@gmail.com last updated on 06/Aug/17

Answered by allizzwell23 last updated on 06/Aug/17

$${\left(\frac{25}{4}\right)}^{3(\mathrm{x}-1)}={\left(\frac{4}{10}\right)}^{3(5-\mathrm{x})}$$$${\left(\frac{5}{2}\right)}^{2(\mathrm{x}-1)}={\left(\frac{2}{5}\right)}^{(5-\mathrm{x})}$$$${\left(\frac{5}{2}\right)}^{2(\mathrm{x}-1)}={\left(\frac{5}{2}\right)}^{-(5-\mathrm{x})}$$$$\Rightarrow 2(\mathrm{x}-1)=\mathrm{x}-5$$$$\therefore \mathrm{x}=-3$$$$$$$$$$

Answered by ajfour last updated on 06/Aug/17

$${(6.25)}^{(3\mathrm{x}-3)}={(0.064)}^{(5-\mathrm{x})}$$$$\Rightarrow {\left(\frac{25}{4}\right)}^{3\mathrm{x}-3}={\left(\frac{8}{25}\right)}^{5-\mathrm{x}}$$$$\Rightarrow {\left(\frac{5}{2}\right)}^{6\mathrm{x}-6}={\left(\frac{2}{5}\right)}^{15-3\mathrm{x}}$$$$\Rightarrow {\left(\frac{5}{2}\right)}^{6\mathrm{x}-6}={\left(\frac{5}{2}\right)}^{3\mathrm{x}-15}$$$$\mathrm{or}6\mathrm{x}-6=3\mathrm{x}-15$$$$\Rightarrow \mathrm{x}=-3.$$

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