Question

Jika H(x) = log (1-x) / (1+x)
buktikan, H(a) + H(b) = H ( a+b / 1+ab )

Answer 1

H(x) = log ((1-x)/(1+x))

H(a) = log ((1-a)/(1+a))
H(b) = log ((1-b)/(1+b))

H((a+b)/(1+ab)) = log((1- ((a+b)/(1+ab)))/((1+((a+b)/(1+ab)))
= log (1 + ab - a - b)/(1 + ab + a + b)

H(a)+H(b) = log((1-a)/(1+a)) + log((1-b)/(1+b))
= log ((1-a)/(1+a) . (1-b)/(1+b)
= log ((1- a - b + ab)/(1 + a + b + ab))

Terbukti bahwa H(a) + H(b) = H((a+b)/(1+ab))