Question

Rezolvati:
log 1/2 (4x+5)=0

Answer 1

Prima data trebuia pusa conditia ca 4x+5>0, deci x>-5/4

log1/2 (4x+5)= log1/2 1

4x+5=1
4x=-4
x=-1

Answer 2

$\displaystyle \mathtt{ log_{ \frac{1}{2}} (4x+5)=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C.E.~4x+5\ \textgreater \ 0}\\ \\ \mathtt{log_{ \frac{1}{2} }(4x+5)=log_{ \frac{1}{2} }1}\\ \\ \mathtt{4x+5=1}\\ \\ \mathtt{4x=1-5}\\ \\ \mathtt{4x=-4}\\ \\ \mathtt{x=-1} \\ \\ \mathtt{x=-1 \Rightarrow 4 \cdot (-1)+5\ \textgreater \ 0~A \Rightarrow x=-1~este~solutie~a~ecuatiei} \\ \\ \mathtt{S=\{-1\}}$