Question

lg3√2×(x−5)＋lg3√2×(x+12)≦2

Answer 1

$mathtt{lg3sqrt{2}(x-5)+lg3sqrt{2}(x+12)leq2;~lg3sqrt{2}[(x-5)+(x+12)]leq2;~}\mathtt{lg3sqrt{2}(2x+7)leq2;~2x+7leqfrac{2}{lg3sqrt{2}}=frac{lg100}{lg3sqrt{2}};~2xleqfrac{lg100}{lg3sqrt{2}}-7;~}\mathtt{2x leq log_{3sqrt{2}}100-7=2log_{18}100-7;~x leq log_{18}100-3,5}$