Question

4^x+16^x=2 ecutatii exponentiale

Answer 1

$4^x=t,t\ \textgreater \ 0 \\ t^2+t-2=0 \\ t_{1}=-2; t_{2}=1 \\ 4^x=1 \\ x=0$

Answer 2

Scriem pe 16 = 4²
4^x + (4^2)^x = 2
(4^x)^2 + 4^x -2=0
Notam 4^x=t
t² + t -2 = 0
t² -t+ 2t -2 = 0
t(t -1)+ 2(t -1) = 0
(t-1)(t+2)=0
t1=1 ⇒4^x=1 ⇒x=0
t2=-2 ⇒4^x=-2 - imposibil.
Solutia este x=0