Question

a square +b square =7ab,prove that,2log (a+b)/3=log a +log b​

Answer 1

Answer:

a²+b²=7ab    →  (1)

LHS=2log(a+b)/3

 =2[log(a+b) - log3]

 =log(a+b)² - log(3)²

 =log(a²+b²+2ab) - log9

 =log9ab - log9                                [From (1)]

 =log(9ab/9)

 =log(ab)

 =log a + log b =RHS

 HENCE VERIFIED

 I hope you know the logarithmic identities used in the above steps. Still I am writing then down here..

1) log(a/b) = log a - log b

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

3) log aˣ = x (log a)