2 ∗ 4 x − 9 ∗ 2 x + 4 = 0 {\displaystyle 2*4^{x}-9*2^{x}+4=0}
2 ∗ 4 x − 9 ∗ 2 x + 4 = 0 2 ∗ 2 2 x − 3 2 ∗ 2 x + 2 x = 0 t = 2 x 2 t 2 − 9 t + 4 = 0 9 ± 81 − 4 ∗ 4 ∗ 2 4 t 1 = 4 t 2 = 1 2 2 x = 4 2 x = 1 2 2 x = 2 2 2 x = 2 − 1 x = 2 x = − 1 {\displaystyle {\begin{aligned}2*4^{x}-9*2^{x}+4=0\\2*2^{2x}-3^{2}*2^{x}+2^{x}=0\\t=2^{x}\\2t^{2}-9t+4=0\\{\frac {9\pm {\sqrt {81-4*4*2}}}{4}}\\t_{1}=4\ \ \ t_{2}={\frac {1}{2}}\\2^{x}=4\ \ \ \ \ 2^{x}={\frac {1}{2}}\\2^{x}=2^{2}\ \ \ \ \ 2^{x}=2^{-1}\\x=2\ \ \ \ \ x=-1\end{aligned}}}
