58 баллов. Найти корень(и) уравнение.1) 5^2x - 3^x

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58 баллов. Найти корень(и) уравнение.
1) 5^2x - 3^x - 15 * 25^x + 15 * 3^x = 0
2) 5^x+1 - 0,2^2-x = 31

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$\displaystyle 5^{2x}-3^x-15*25^x+15*3^x=0\\\\5^{2x}-3^x-15*5^{2x}+15*3^x=0\\\\5^{2x}(1-15)-3^x(1-15)=0\\\\-14(5^{2x}-3^x)=0\\\\5^{2x}=3^x\\\\x=0$

$\displaystyle 5^{x+1}-0.2^{2-x}=31\\\\5*5^x-(\frac{1}{5})^2*(\frac{1}{5})^{-x}=31\\\\5*5^x-\frac{1}{25}*5^x=31\\\\5^x(5-\frac{1}{25})=31\\\\5^x=\frac{31*25}{124}\\\\5^x=6.25\\\\5^x=\frac{625}{100}\\\\5^x=\frac{5^4}{5^2*4}\\\\5^x=\frac{5^2}{4}\\\\x=log_5(\frac{5^2}{4})=2-log_54$

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