Question

if x^2+y^2=74xy then show that 2log(x-y)=3log2+2log3+logx+logy​

Answer 1

x² + y² can be also written as (x-y)² +2xy So,

(x-y)² + 2xy = 74xy

(x-y)² = 72xy

Now taking log on both sides

2log(x-y) = log(72xy)

= log72 + logx + logy

Now 72 = 8 x 9 = 2³ x 3² So,

2log(x-y) = log2³ + log3²+ logx + logy

= 3log2 + 2log3+ logx + logy