Question

Va rog ajutati ma ex 2 punctul a atat va rog frumos e urgent dau coroana si stele

Answer 1

Răspuns:

3

Explicație pas cu pas:

$log_{2}(2^{x}+1)+log_{0,5}(4^{x}-55)=0,~=>~log_{2}(2^{x}+1)+log_{2^{-1}}(4^{x}-55)=0,~=>~log_{2}(2^{x}+1)+\frac{1}{-1} log_{2}(4^{x}-55)=0,~=>~log_{2}(2^{x}+1)-log_{2}(4^{x}-55)=0,~=>~log_{2}\dfrac{2^{x}+1}{4^{x}-55}=0,~=>~\dfrac{2^{x}+1}{4^{x}-55}=2^{0},~\dfrac{2^{x}+1}{4^{x}-55}=1,~=>4^{x}-55=2^{x}+1,~=>~4^{x}-2^{x}-56=0\\Fie~2^{x}=t>0,~=>~4^{x}=(2^{t})^{2}=t^{2}.~~Obtinem~ecuatia~t^{2}-t-56=0$

Δ=(-1)²-4·1·(-56)=1+224=225>0, deci t1=(1-15)/2=-7 care nu convine deoarece t>0

t2=(1+15)/2=8, care convine

Deci 2ˣ=8, ⇒x=3.

Verificarea o las pe seama ta... :))), dar convine.