Question

3×16^{x}+2×81^{x}=5×36^{x}
15 баллов

Answer 1

$\displaystyle 3*16^x+2*81^x=5*36^x\\\\2*9^{2x}-5*(9*4)^x+3*4^{2x}=0|4^{2x}\\\\ 2*(\frac{9}{4})^{2x}-5*(\frac{9}{4})^x+3=0\\\\ (\frac{9}{4})^x=t\\\\2t^2-5t+3=0\\\\D=25-24=1\\\\t_{1.2}= \frac{5\pm 1}{4}\\\\t_1= \frac{6}{4}= \frac{3}{2}; t_2=1$

$\displaystyle (\frac{9}{4})^x= \frac{3}{2}\\\\ (\frac{3}{2})^{2x}= \frac{3}{2}\\\\2x=1\\\\x= \frac{1}{2}$

$\displaystyle (\frac{9}{4})^x=1\\\\x=0$

Ответ  х=0; х=1/2