Question

log(a-b)= 1/2 log(5ab), show that asquare +bsquear​

Answer 1

Given :

• log (a-b) = (1/2) log (5ab)

To prove : a² + b² = 7ab

Identity used :

• (a-b)² = a² + b² + 2ab

$\bullet \sf \: log( {a}^{m} ) = m \: log(a)$

$\bullet \sf \: if \: log(a) = log(b) \implies \: a = b$

Solution :

log (a-b) = (1/2) log 5ab

=> 2 log (a-b) = log 5ab

using identity,

=> log (a-b)² = log 5ab

=> (a-b)² = 5ab

=> a² + b² - 2ab = 5ab

=> a² + b² = 5ab + 2ab

=> a² + b² = 7ab

HENCE PROVED