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Question Number 59730 by muneshkumar last updated on 14/May/19

$$5^{2x-1}={25}^{x-1}+100findvalueof{3}^{3-x}$$

Answered by tanmay last updated on 14/May/19

$$\frac{5^{2x}}{5}={\left(5^2\right)}^{x-1}+100$$$$\frac{{\left(5^x\right)}^2}{5}=\frac{5^{2x}}{5^2}+100$$$$5^x=a$$$$\frac{a^2}{5}=\frac{a^2}{25}+100$$$$\frac{a^2}{5}-\frac{a^2}{25}=100$$$$\frac{5a^2-a^2}{25}=100$$$$4a^2=100\times 25$$$$a^2={\left(\frac{10\times 5}{2}\right)}^2=5^4$$$$5^{2x}=5^4$$$$2x=4$$$$x=2$$$$so$$$$3^{3-2}$$$$3^{3-2}$$$$3^1$$$$3$$$$$$$$$$

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