Question

Выразите через a и b значение log80(200), если log11(2)=a ; log11(5)=b.

Answer 1

$log_{80}200=\frac{log_{11}200 }{log_{11}80}=\frac{log_{11}(8*25) }{log_{11}(5*16)}=\frac{log_{11}2^{3}+log_{11}5^{2}}{log_{11} 5+log_{11}2^{4}}=\frac{3log_{11}2+2log_{11}5}{log_{11}5+4log_{11}2}=\frac{3a+2b}{b+4a}$