Question

Hi, solve this

$if \: {x}^{2} + {y}^{2} = 25xy \: then \: prove \: that \: 2log \:( x + y) = 3log3 + logx + logy$

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Answer 1

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Here is your answer:
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${x}^{2} + {y}^{2} = 25xy \\ \\ add \: 2xy \: on \: both \: sides \\ \\ {x}^{2} + {y}^{2} + 2xy = 25xy + 2xy \\ \\ {(x + y) }^{2} = 27xy \\ \\ take \: log \: on \: both \: sides \\ \\ log {(x + y)}^{2} = log29xy \\ \\ log {(x + y)}^{2} = log {3}^{3} + logx + logy \\ \\ 2logx = 3log3 + logx + logy \\ \\ hence \: proved.....$

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