Question

log(14)7=a, log(14)5=b. Найдите log(28)35

Answer 1

$log_{28}35= \frac{log_{14}35}{log_{14}28} = \frac{log_{14}(7*5)}{log_{14}(14*2)} = \\ \\ = \frac{log_{14}7+log_{14}5}{log_{14}14+log_{14}2} = \frac{a+b}{1+ log_{14}(14/7)} = \\ \\ = \frac{a+b}{1+log_{14}14-log_{14}7} = \frac{a+b}{1+1-a} = \frac{a+b}{2-a}$