0 \wedge 3x-1>0\\ x>5 \wedge 3x>1\\ x>5 \wedge x>\frac{1}{3}\\ x>5\\\\ \lg5(x-5)=\lg(3x-1)\\ 5(x-5)=3x-1\\ 5x-25=3x-1\\ 2x=24\\ x=12 " alt="\\\lg(x-5)+\lg5=\lg(3x-1)\\ x-5>0 \wedge 3x-1>0\\ x>5 \wedge 3x>1\\ x>5 \wedge x>\frac{1}{3}\\ x>5\\\\ \lg5(x-5)=\lg(3x-1)\\ 5(x-5)=3x-1\\ 5x-25=3x-1\\ 2x=24\\ x=12 " align="absmiddle" class="latex-formula">