Question Number 10064 by PradipGos. last updated on 22/Jan/17

if a^2 +b^2 =3ab then prove that log((a+b)/(√5))=(1/2)(loga+logb)

Answered by ridwan balatif last updated on 22/Jan/17

a^2 +b^2 =3ab→(a+b)^2 −2ab=3ab→a+b=±(√(5ab)) we take a+b=+(√(5ab)) log((a+b)/(√5))=log(((√5)×(√(ab)))/(√5)) =log(√(ab)) =log(ab)^(1/2) =(1/2)log(ab) =(1/2)(loga + logb) (Terbukti)