Question

Зная, что log(3,6)=a, log(5,6)=b, log(105,6)=c, найдите log(7,6)

Answer 1

 
    
    $log_{3}6 = a\\ log_{5}6=b\\ log_{105}6=c\\\\ log_{7}6 = \frac{1}{log_{6}7} \\\\ log_{6}3=\frac{1}{a}\\ log_{6}5=\frac{1}{b}\\ log_{6}105=\frac{1}{c} \\\\ \\ log_{6}105 = log_{6}(3*7*5) = log_{6}3+log_{6}7+log_{6}5 = \frac{1}{c}\\ log_{6}7 = \frac{1}{c} - \frac{1}{a} - \frac{1}{b} \\ log_{7}6= \frac{abc}{ ab-bc-ac}$