Question

If x2+y2=23xy, then 2log(x+y)=

Answer 1

$heya \\ \\ \\ \\ x {}^{2} + y {}^{2} = (x + y) {}^{2} - 2xy = 23xy \\ \\ \\ \\ (x + y) {}^{2} = 25xy \\ \\ \\ \\ taking \: log \: on \: both \: sides \\ \\ \\ \\ log(x + y) {}^{2} = log(5 {}^{2} \times x \times y) \\ \\ \\ \\ 2 log(x + y) = 2 log(5) + log(x) + log(y)$

Answer 2

2log(x+y)

=log(x+y)^2

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

=log(23xy + 2xy) [ x2+y2=23xy]

=log(25xy)

=log25 +logxy