Question

\(4^x-10\times2^x+16=0\)

Answer 1

\(4^x-10.2^x+16=0\)

\(\Leftrightarrow\left(2^x\right)^2-10.2^x+16=0\)

Đặt 2^x = t

\(\Rightarrow t^2-10t+16=0\)

\(\Leftrightarrow t^2-2t-8t+16=0\)

\(\Leftrightarrow t\left(t-2\right)-8\left(t-2\right)=0\)

\(\Leftrightarrow\left(t-2\right)\left(t-8\right)=0\)

\(\Rightarrow\left\{{}\begin{matrix}t=2\\t=8\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2^x=2\\2^x=8\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)