1.
0\\ 2x>-5\\ x>-\frac{5}{2}\\\\ \log_{\frac{1}{3}}(2x+5)<\log_{\frac{1}{3}}\left(\frac{1}{3}\right)^0\\ 2x+5>{\left(\frac{1}{3}\right)}^0\\ 2x+5>1\\ 2x>-4\\ x>-2\\\\ x>-\frac{5}{2} \wedge x>-2\\ \underline{x>-2} " alt=" \\\log_{\frac{1}{3}}(2x+5)<0\\ 2x+5>0\\ 2x>-5\\ x>-\frac{5}{2}\\\\ \log_{\frac{1}{3}}(2x+5)<\log_{\frac{1}{3}}\left(\frac{1}{3}\right)^0\\ 2x+5>{\left(\frac{1}{3}\right)}^0\\ 2x+5>1\\ 2x>-4\\ x>-2\\\\ x>-\frac{5}{2} \wedge x>-2\\ \underline{x>-2} " align="absmiddle" class="latex-formula">
2.
-1\\ 3-4x>0\\ -4x>-3\\ x<\frac{3}{4}\\\\ \log_{\frac{1}{4}}(3-4x)>\log_{\frac{1}{4}}\left(\frac{1}{4}\right)^{-1}\\ 3-4x<{\left(\frac{1}{4}\right)}^{-1}\\ 3-4x<4\\ -4x<1\\ x>-\frac{1}{4}\\\\ x<\frac{3}{4} \wedge x>-\frac{1}{4}\\ \underline{x\in(-\frac{1}{4},\frac{3}{4})} " alt=" \\\log_{\frac{1}{4}}(3-4x)>-1\\ 3-4x>0\\ -4x>-3\\ x<\frac{3}{4}\\\\ \log_{\frac{1}{4}}(3-4x)>\log_{\frac{1}{4}}\left(\frac{1}{4}\right)^{-1}\\ 3-4x<{\left(\frac{1}{4}\right)}^{-1}\\ 3-4x<4\\ -4x<1\\ x>-\frac{1}{4}\\\\ x<\frac{3}{4} \wedge x>-\frac{1}{4}\\ \underline{x\in(-\frac{1}{4},\frac{3}{4})} " align="absmiddle" class="latex-formula">
3.
\frac{1}{2}\\ 4x+3>0\\ 4x>-3\\ x>-\frac{3}{4}\\\\ \log_{16}(4x+3)>\log_{16}16^{\frac{1}{2}}\\ 4x+3>16^{\frac{1}{2}}\\ 4x+3>4\\ 4x>1\\ x>\frac{1}{4}\\\\ x>\frac{1}{4} \wedge x>-\frac{3}{4}\\ \underline{x>\frac{1}{4}} " alt=" \\\log_{16}(4x+3)>\frac{1}{2}\\ 4x+3>0\\ 4x>-3\\ x>-\frac{3}{4}\\\\ \log_{16}(4x+3)>\log_{16}16^{\frac{1}{2}}\\ 4x+3>16^{\frac{1}{2}}\\ 4x+3>4\\ 4x>1\\ x>\frac{1}{4}\\\\ x>\frac{1}{4} \wedge x>-\frac{3}{4}\\ \underline{x>\frac{1}{4}} " align="absmiddle" class="latex-formula">
4.
0\\ -5x>-12\\ x<\frac{12}{5}\\\\ \lg(12-5x)<\lg10^0\\ 12-5x<10^0\\ 12-5x<1\\ -5x<-11\\ x>\frac{11}{5}\\\\ x>\frac{11}{5} \wedge x<\frac{12}{5}\\ \underline{x\in(\frac{11}{5},\frac{12}{5})}" alt=" \\\lg(12-5x)<0\\ 12-5x>0\\ -5x>-12\\ x<\frac{12}{5}\\\\ \lg(12-5x)<\lg10^0\\ 12-5x<10^0\\ 12-5x<1\\ -5x<-11\\ x>\frac{11}{5}\\\\ x>\frac{11}{5} \wedge x<\frac{12}{5}\\ \underline{x\in(\frac{11}{5},\frac{12}{5})}" align="absmiddle" class="latex-formula">