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Question Number 17779 by Mr easymsn last updated on 10/Jul/17

s h o w t h a t {l o \underset{a}{g a b}} {l o \underset{b}{g a b}} = l o g a \underset{a}{b} + l o g a \underset{b}{b}

Answered by Tinkutara last updated on 11/Jul/17

(\log_{a} a b) (\log_{b} a b)

= (1 + \log_{a} b) (1 + \log_{b} a)

= 1 + \log_{b} a + \log_{a} b + 1

= \log_{b} b + \log_{b} a + \log_{a} b + \log_{a} a

= \log_{a} a b + \log_{b} a b