Question

Rez ecuația : 4 la puterea x -3.2la x-28=0

Answer 1

[tex]4^x-3\cdot 2^x-28=0\\ (2^x)^2-3\cdot 2^x-28=0\\ Notam:2^x=t\ \textgreater \ 0\\ t^2-3\cdot t-28=0\\ \Delta=9+4\cdot 28=121\Rightarrow \sqrt{\Delta}=11\\ t_1=\dfrac{3+11}{2}=7\\ t_2=\dfrac{3-11}{2}=-4\ \textless \ 0\\ 2^x=7\Rightarrow x=\log_27 [/tex]

Answer 2

[tex]\it 4^x-3\cdot2^x-28=0 \Rightarrow (2^x)^2-3\cdot2^x-28=0 \\\;\\ Notez\ 2^x=t,\ t\ \textgreater \ 0. \\\;\\ Acum,\ avem: \ \ t^2-3t-28=0 \Rightarrow t=7 \Rightarrow 2^x=7 \Rightarrow \\\;\\ log_22^x=log_27 \Rightarrow x\cdot log_2 2=log_2 7 \Rightarrow x\cdot 1=log_2 7 \Rightarrow x=log_2 7 [/tex]