Question

if log a+log b=log(a^2+b^2) then proved that (a+b) ^2=3ab​

Answer 1

Hey Buddy

Here's The Answer

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Given :

log a + log b = log ( a² + b² )

To prove : ( a + b )² = 3ab

Solution :We know, log x + log y = log ( xy )

=> log a + log b = log ( a² + b² )

By using above logarithm property

=> log ( ab ) = log ( a² + b² )

Cancelling log both sides.

ab = a² + b²

adding 2ab on both sides

ab + 2ab = a² + b² + 2ab

on R.H.S, ( a² + b² + 2ab ) can be written as ( a + b )²

ab + 2ab = ( a + b )² 3ab = ( a + b )²

Hence Proved.

Hope It Helps.