if a^2 + b^2 = 6 ab then show log a - b / 2 =1/2 ( log a + log b )
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a^2 + b^2 =6ab
(a -b)^2 +2ab = 6ab
(a - b)^2 = 4ab
take log both sides
log(a - b)^2 =log4ab
2log(a -b) =log4 +loga +logb
2log(a - b) =2log2 +loga + logb
log(a - b) = log2 +1/2(loga + logb )
log(a -b)-log2 =1/2(loga +logb )
log(a - b)/2 =1/2(loga + logb )
(a -b)^2 +2ab = 6ab
(a - b)^2 = 4ab
take log both sides
log(a - b)^2 =log4ab
2log(a -b) =log4 +loga +logb
2log(a - b) =2log2 +loga + logb
log(a - b) = log2 +1/2(loga + logb )
log(a -b)-log2 =1/2(loga +logb )
log(a - b)/2 =1/2(loga + logb )
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