Question

高等数学求解，谢谢

Answer 1

x->0
ln(1+x) ~ x
a^x ~ 1 + (lna)x
b^x ~ 1 + (lnb)x
a^x-b^x ~ [ln(a/b)]x

lim(x->0) (a^x -b^x)/ln(1+x)
=lim(x->0) [ln(a/b)]x/x
=ln(a/b)