Question

Prove that 3log(a + b) = log(a+b) + 2loga + log(1 + 2b/a + b^2/a^2)

Answer 1

Answer:

Log (a + b)/2 = 1/2 (Log a + Log b)

=> Log (a + b)/2 = 1/2 Log ab

=> Log (a + b)/2 = Log ab^(1/2)

=> (a + b)/2 = ab^(1/2)

=> (a^2 + b^2 + 2ab)/4 = ab

=> a^2 + b^2 + 2ab = 4ab

=> a^2 + b^2 - 2ab = 0

=> (a - b)^2 = 0

=> a - b = 0

=> a = b