Question

If log x^2 + y ^2 = 25xy then prove that 2log ( x+y) = 3log3 + log x + log y

Answer 1

HEYA!!!!

Given,

${x}^{2} + {y}^{2} = 25xy$

Add 2xy on both sides.

${x}^{2} + {y}^{2} + 2xy = 25xy + 2xy$

${(x + y)}^{2} = 27xy$

Take log on both sides.

$log {(x + y)}^{2} = log27xy$

log xyz = log x + log y + log z


$log {(x + y)}^{2} = log \: {3}^{3} + log \: x \: + log \: y$

$log {x}^{m} = m \: log \: x$

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


Hence, proved..


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