Question

If a²+b² =7ab prove.
2log (a+b) = log9 + log a + log b​

Answer 1

Solution :

Given :

a² + b² = 7ab

Adding 2ab on both sides

⇒ a² + b² + 2ab = 7ab + 2ab

⇒ (a + b)² = 9ab

[ Because (a + b)² = a² + b² + 2ab ]

Taking log on both sides

⇒ log (a + b)² = log 9ab

⇒ 2log (a + b) = log 9ab

[ Because log a^n = nlog a ]

⇒ 2log (a + b) = log9 + log a + log b

[ Because log a + log b = log ab ]

Hence proved.