a^2+c^2=b^2+ac
a^2+c^2-b^2=ac
cosB=(a^2+c^2-b^2)/2ac
=ac/2ac
=1/2
B=60°
log4(sinA)+log4(sinC)=-1
log4(sinAsinC)=-1
sinAsinC=1/4
-[cos(A+C)-cos(A-C)] /2=1/4
cos(A+C)-cos(A-C)=-1/2
cos(180-B)-cos(A-C)=-1/2
-cosB-cos(A-B)=-1/2
-1/2-cos(A-B)=-1/2
cos(A-B)=0
A=B=60°
所以A=B=C=60°
a=b=c
S△ABC=1/2acsinB
√3=1/2ac*√3/2
ac=4
a=c
a^2=4
a=2
所以a=b=c=2