[tex]\displaystyle log_5(2x+3)=log_24 \\ 2x+3\ \textgreater \ 0 \Rightarrow x\ \textgreater \ - \frac{3}{2} ~~~~~~~~~~~x \in \left (- \frac{3}{2}, \infty \right ) \\ log_5(2x+3)=log_22^2 \\ log_5(2x+3)=2log_22 \\ log_5(2x+3)=2 \\ log_5(2x+3)=log_55^2 \\ 2x+3=5^2 \\ 2x+3=25 \\ 2x=25-3 \\ 2x=22 \\ x= \frac{22}{2} \\ x=11 [/tex]
