Question

lg3√2×(x−5)＋lg3√2×(x+12)≦2

Answer 1

$\mathtt{lg3\sqrt{2}(x-5)+lg3\sqrt{2}(x+12)\leq2;~lg3\sqrt{2}[(x-5)+(x+12)]\leq2;~}\\\mathtt{lg3\sqrt{2}(2x+7)\leq2;~2x+7\leq\frac{2}{lg3\sqrt{2}}=\frac{lg100}{lg3\sqrt{2}};~2x\leq\frac{lg100}{lg3\sqrt{2}}-7;~}\\\mathtt{2x \leq log_{3\sqrt{2}}100-7=2log_{18}100-7;~x \leq log_{18}100-3,5}$