Question

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

Answer 1

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