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)