Question from http://www.sgforums.com/forums/2297/topics/309850
Given that logb(xy2) = m and logb (x3y)= n, express logb y/x and logb √(xy) in terms of m and n.
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Answer:
(1): logb (xy2) =m
(2): logb (x3y)=n
(1) becomes logb x + 2 logb y = m
(2) becomes 3 logb x + logb y = n
2 * (2) – (1) : 5 logb x = 2n – m
(3): logb x = 0.2 (2n – m) = 0.4n – 0.2m
Thus,
(4): logb y = n – 3 logb x = 0.6m – 0.2n
And hence,
logb y/x = logb y - logb x = 0.8m – 0.6n
logb √(xy) = 0.5 (logb x + logb y) = 0.2m + 0.1n
