giúp cho câu 3 nhé: $\Leftrightarrow 8-2^x.x+2^3.2^{-x}-x=0$$\Leftrightarrow 8.2^x-2^{2x}.x+2^3-2^x.x=0$$\Leftrightarrow (2^x+1).(8-2^x.x)=0$$\Leftrightarrow \left[ {\begin{matrix}2^x+1=0 (VN)\\8-2^x.x=0 \end{matrix}} \right.$$\Leftrightarrow 2^x.x=8$$\Leftrightarrow log_2x=3-x(3)$Đặt $t=log_2x\Rightarrow x=2^t$$(3)\Leftrightarrow 2^t+t=3 $(*)xét $f(t)=2^t+t, t\in R$ $f'(t)=2^t+1>0\Rightarrow f(t)$đồng biến (*) có duy nhất 1 nghiệmmà $f(1)=3\Rightarrow t=3=log_2x$ $\Rightarrow x=2$
giúp cho câu 3 nhé: $\Leftrightarrow 8-2^x.x+2^3.2^{-x}-x=0$$\Leftrightarrow 8.2^x-2^{2x}.x+2^3-2^x.x=0$$\Leftrightarrow (2^x+1).(8-2^x.x)=0$$\Leftrightarrow \left[ {\begin{matrix}2^x+1=0 (VN)\\8-2^x.x=0 \end{matrix}} \right.$$\Leftrightarrow 2^x.x=8$$\Leftrightarrow log_2x=3-x$Đặt $t=log_2x\Rightarrow x=2^t$$\Leftrightarrow 2^t+t=3 $(*)xét $f(t)=2^t+t, t\in R$ $f'(t)=2^t+1>0\Rightarrow f(t)$đồng biến (*) có duy nhất 1 nghiệmmà $f(1)=3\Rightarrow t=3=log_2x$ $\Rightarrow x=2$
giúp cho câu 3 nhé: $\Leftrightarrow 8-2^x.x+2^3.2^{-x}-x=0$$\Leftrightarrow 8.2^x-2^{2x}.x+2^3-2^x.x=0$$\Leftrightarrow (2^x+1).(8-2^x.x)=0$$\Leftrightarrow \left[ {\begin{matrix}2^x+1=0 (VN)\\8-2^x.x=0 \end{matrix}} \right.$$\Leftrightarrow 2^x.x=8$$\Leftrightarrow log_2x=3-x
(3)$Đặt $t=log_2x\Rightarrow x=2^t$$
(3)\Leftrightarrow 2^t+t=3 $(*)xét $f(t)=2^t+t, t\in R$ $f'(t)=2^t+1>0\Rightarrow f(t)$đồng biến (*) có duy nhất 1 nghiệmmà $f(1)=3\Rightarrow t=3=log_2x$ $\Rightarrow x=2$