Question

Выразите log28 35 через a и b , если log14 7=a, log14 5=b

Answer 1

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