Question

3×16^{x}+2×81^{x}=5×36^{x}
15 баллов

Answer 1

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

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

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

Ответ  х=0; х=1/2