0, \ x>-3
\\
\\lg(x+3)>lg1
\\
\\x+3>1
\\
\\x>-2
\\
\\x\in(-2,+\infty)
\\
\\2sinx-1=0
\\
\\sinx=\frac12
\\
\\x=\frac\pi6+2n\pi \ \vee \ x=(\pi-\frac\pi6)+2n\pi=\frac{5\pi}{6}+2n\pi, \ n\in Z" alt="\\lg(x+3)>0, \ x>-3
\\
\\lg(x+3)>lg1
\\
\\x+3>1
\\
\\x>-2
\\
\\x\in(-2,+\infty)
\\
\\2sinx-1=0
\\
\\sinx=\frac12
\\
\\x=\frac\pi6+2n\pi \ \vee \ x=(\pi-\frac\pi6)+2n\pi=\frac{5\pi}{6}+2n\pi, \ n\in Z" align="absmiddle" class="latex-formula">