Question

ifx2+y2=25xyprove that 2log (x-y)=log23+logxlogy

Answer 1

x² + y² = 25xy

(x - y)² +2xy = 25xy

(x - y)² = 23xy

take log both sides ,

log(x -y)² = log(23xy)

2log(x - y) = log23 + logx + logy

2log(x -y) = log23 + logx + logy

2log(x - y) = log23 + Iogx + logy

log( x - y) = 1/2{ log23 + logx + logy }

here something typing mistake ,
I think question is
if x² + y² = 25xy
then , proved that
log(x - y) = 1/2{log23 + logx + logy }