Question

If x2+y2=18xy, then prove that 2log(x + y) = 2log 2+ log 5 + log x+ log y.

Answer 1

Answer:

$given \\ \: \: \: \: {x}^{2} + {y}^{2} = 18xy \\ 2 log(x + y) = 2 log(2) + log(5) + log(x) + log(y) \\ log(x + y)^{2} = log( {x}^{2} + {y}^{2} + 2xy) \\ = log(18xy + 2xy) \\ = log(20 xy) = log(4 \times 5 \times x \times y ) \\ = log(4) + log(5) + log(x) + log(y) \\ = log( {2}^{2} ) + log(5) + log(x) + log(y) \\ = 2 log(2) + log(5) + log(x) + log(y)$