Question

Prove that :  If a log b + b log a - 1 = 0, then b^a. a^b = 10

Answer 1

Given that

a log b + b log a - 1 = 0

⇒ a log b + b log a  = 1 

⇒ log b^a + loga^b =1

⇒ log b^a + log a^b = log 10

⇒ log ( b^a . a^b ) = log 10

⇒ b^a . a^b = 10