Question

Решить уравнение
$3*4^{x}-11*2^{x}=4$

Answer 1

$3*4^{x}-11*2^{x} =4\\\\3*(2^{x})^{2}-11*2^{x}-4=0\\\\2^{x}=m,m>0\\\\3m^{2}-11m-4=0\\\\D=(-11)^{2}-4*3*(-4)=121+48=169=13^{2}\\\\m_{1}=\frac{11+13}{6} =4\\\\m_{2}=\frac{11-13}{6}=-\frac{1}{3}<0-neyd\\\\2^{x}=4\\\\2^{x}=2^{2}\\\\x=2\\\\Otvet:\boxed{2}$