Question

a2+b2=7ab then prove the 2log(a+b)=log a+log b+2log3

Answer 1

By using properties of logarithm,

2log(a+b)=log(a+b)²=log(a²+2ab+b²)

Now put a²+b²=7ab

=log(9ab)=2log3+log a + log b

Answer 2

Given that a2+b2=7ab
                   adding 2ab on both sides . we get
                         a2+b2+2ab=9ab    
                     it can be written as (a+b)2 
then               (a+b)2= 3^(2) ab
                             applying log on both sides we get
                         log(a+b)^2 = log3(^2)ab
                             so,
                            2log(a+b)=log a+log b+ 2log3      [since log m^n= n log m]
           hence proved