A+C=2B,==> B=60,log4sinA+log4sinC=-1 ==> sinAsinC = 1/4
面积 = 根号3 = a*b*sinC/2 ...(1)
面积 = 根号3 = b*c*sinA/2 ...(2)
面积 = 根号3 = c*a*sinB/2 = c*a*[(根号3)/2]/2...(3)
(3):==> c*a = 4 ...(4)
(1)*(2):12 = a*b^2*c*(sinAsinC) = a*b^2*c*(1/4) = b^2 ==> b=2*根号3
b^2 = a^2 + c^2 - 2ac*cosB ===> a^2 + c^2 = 16 ...(5)
(4)(5):a = 根号6 + 根号2,c = 根号6 - 根号2
因此:三条边长分别为:a = 根号6 + 根号2;b=2*根号3;c = 根号6 - 根号2.