Question

Дано: lg3=a, lg5b. Найдите log15 30

Answer 1

$log_{15}30 = log_{15}10 + log_{15}3 = frac{lg10}{lg15} + frac{log_{3}3}{log_315} = frac{1}{lg3 + lg5} + frac{1}{log_33+log_35} =\ = frac{1}{a+b} + frac{1}{1+ frac{lg5}{lg3} } = frac{1}{a+b} + frac{1}{1+ frac{b}{a} } = frac{1}{a+b} + frac{a}{a+b} = frac{1+a}{a+b}$