Question

x2+y2=25xy then show that 2log (x+y)=2log+logx+logy

Answer 1

the question actually is 3 log3

${x}^{2} + {y}^{2} = 25xy \\ add \: 2xy \: on \: both \: sides \: to \: make \\ \: it \: {(x + y)}^{2}$

${x}^{2} + {y}^{2} + 2xy = 25xy + 2xy \\ {(x + y)}^{2} = 27xy$

add log on both sides

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

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