Q5 of 54 Page 22

If x2 + y2 = 25xy, then prove that 2 log(x + y) = 3log3 + logx + logy.

x2 + y2 = 25xy


Adding 2xy on both sides


x2 + y2 + 2xy = 27xy


(x + y)2 = 27xy


Taking log both sides


log (x + y)2 = log 27xy


2 log (x + y) = log 27 + log x + log y


2 log(x + y) = log 33 + log x + log y


2 log (x + y) = 3 log 3 + log x + log y


Hence proved.


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