如何证明lim(x→0)(a^x-1)/(xlna)=1 用重要极限

令t=a^x-1,则x=log(a)(1+t),
∴原式=(lim(t→0)(t/log(a)(1+t)))/lna
=(lim(t→0)(1/log(a)((1+t)^(1/t))))/lna
=(1/log(a)(e))/lna
=1.用洛必达法则呢原式=lim(x→0)(a^x·lna/lna)=1