Question

If x 2

+ y 2

= 27 xy then prove that 2 log (x –y) = 2 log 5 + log x + log y​

Answer 1

Step-by-step explanation:

x^{2} + y^{2} = 27xyx

2

+y

2

=27xy

To prove ,

2log(x-y) = 2log5 + logx + logy

Consider ,

x^{2} + y^{2} = 27xyx

2

+y

2

=27xy

Subtract 2xy on both sides of the equation.

x^{2} + y^{2} - 2xy= 27xy-2xyx

2

+y

2

−2xy=27xy−2xy

(x-y)^{2}= 25xy(x−y)

2

=25xy

Apply log on both sides,

Log (x-y)^{2} = log25xy

It can be written as ,

2 log(x-y) = log 5^2 + logx+logy

=> 2 log (x-y) = 2log5 + log x + logy

Hence proved