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Question

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

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Solution

We have,
x2+y2=25xy

x2+y2+2xy=25xy+2xy

(x+y)2=27xy

On taking logarithm, we get
log(x+y)2=log(27xy)

2log(x+y)=log27+logx+logy (logmn=nlogm) and (logmn=logm+logn)

2log(x+y)=log33+logx+logy

2log(x+y)=3log3+logx+logy

Hence, proved.

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