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If x^2+y^2=23 then prove that 2log(x+y)=2log5+logx+logy

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(x+y)2 = x2 + 2xy + y2 = 25xy

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

But, log(x+y)2 = log(25xy)

= log25 + logx + logy

= log(52) + logx + logy

= 2log5 + logx + logy

So, 2log(x+y) = 2log5 + logx + logy

2(log(x+y) - log5) = logx + logy

log(x+y) - log5 = ½[logx + logy]

log{(x+y)/5} = ½[logx + logy]

Please mark me as brainlist

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

But, log(x+y)2 = log(25xy)

= log25 + logx + logy

= log(52) + logx + logy

= 2log5 + logx + logy

So, 2log(x+y) = 2log5 + logx + logy

2(log(x+y) - log5) = logx + logy

log(x+y) - log5 = ½[logx + logy]

log{(x+y)/5} = ½[logx + logy]

Please mark me as brainlist

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