Question

25^x-20^x-2*16^x=0
9 КЛАСС СРОЧНО

Answer 1

$25^x-20^x-2\cdot16^x=0\\5^{2x}-5^x\cdot4^x-2\cdot4^{2x}=0|:4^{2x}\\(\frac{5}{4} )^{2x}-(\frac{5}{4} )^{x}-2=0$

Замена: $(\frac{5}{4} )^{x} = t, t>0$

$t^2-t-2=0\\t_1=-1<0\\t_2=2$

$(\frac{5}{4} )^{x}=2\\1,25^x=2\\x=\log_{1,25}{2}$