∵f(x)是偶函数,∴f(x)-f(-x)=0,
即lg(10^x+1)+ax-{lg[10^(-x)+1]+a(-x)}=0
lg;[(10^x+1)/(10^(-x)+1)]+2ax=0
lg10^x+2ax=0
x+2ax=0
(2a+1)x=0
∴2a+1=0,即a=-1/2.