Question

log in baza 2 (2x+1)=-1

Answer 1

㏒₂(2x+1)=-1⇒
CE:2X+1≥0⇒X≥-1/2
2X+1=2∧-1⇒2X+1=-2⇒2X=-1-2⇒2X=-3⇒X=-3/2
SUCEES

Answer 2

[tex]\log_2(2x+1) = -1 \Rightarrow 2x+1 =2^{-1} \Rightarrow 2x+1 = \dfrac{1}{2}|_{\cdot2} \Rightarrow \\\;\\ \Rightarrow 4x+2=1|_{-2} \Rightarrow 4x=-1 \Rightarrow x= -\dfrac{1}{4} \\\;\\ \it Determinam\ domeniul\ de\ existenta\ a ecuatiei: [/tex]

[tex]2x+1\ \textgreater \ 0 \Longrightarrow 2x\ \textgreater \ -1 \Longrightarrow x \ \textgreater \ -\dfrac{1}{2} \Longrightarrow x \in \left(-\dfrac{1}{2}, \infty \right) \\\;\\ -\dfrac{1}{4}\in \left(-\dfrac{1}{2}, \infty \right) \Longrightarrow x = -\dfrac{1}{4}\ este\ solutie\ a \ ecuatiei\ date.[/tex]