Question

urgent dau 100 puncte inima 5 stele, cel mai bun raspuns. Va rog nu comentati ca nu stiu. Scrie doar rezolvarea exercitiilor atat. calasa a x a​

Answer 1

rezolvarea in anexa foto

Answer 2

11)

$\it 2^x+2^{2x+1}=6 \Rightarrow\ 2^x+2\cdot(2^x)^2-6=0\\ \\ Fie\ 2^x=t,\ t>0,\ iar\ ecua\c{\it t}ia\ devine:\\ \\ 2t^2+t-6=0 \Rightarrow\ 2t^2+4t-3t-6=0 \Rightarrow\ 2t(t+2)-3(t+2)=0 \Rightarrow\ \\ \\ \Rightarrow\ (t+2)(2t-3)=0 \Rightarrow\ \begin{cases} \it t+2=0 \Rightarrow\ t=-2<0,\ nu\ convine\\ \\ \it 2t-3=0 \Rightarrow\ t=\dfrac{3}{2}\end{cases}$

$\it t=\dfrac{3}{2} \Rightarrow\ 2^x=\dfrac{3}{2} \Rightarrow\ 2\cdot2^x=3 \Rightarrow\ 2^{x+1}=3 \Rightarrow\ log_2 2^{x+1}=log_2 3 \Rightarrow\ \\ \\ \Rightarrow\ (x+1)log_2 2=log_2 3 \Rightarrow\ x+1=log_2 3 \Rightarrow\ x=-1+log_2 3$