How do you prove Lim h-0 x^h-1hln x

How do you prove Lim h-->0 (x^h-1)/h=ln x?

according to L'Hopital's rule, you can differentiate the top and bottom if you get plus or minus infinity over infinity or 0 over 0, so you can differentiate top and bottom w/ respect to h

lim h->0 (d(x^h-1)/dh)/(dh/dh)
lim h->0 d(x^h-1)/dh
lim h->0 x^h *ln(x)
ln(x) <---- answer

math rules used besides L'Hopital's described above:
a^0 = 1; a ? 0

d/dx a^x = lna * a^x; a > 0

Other Answers:

Using L'Hospital's Rule: differentiate the top and bottom (with respect to h):

Lim h->0 x^(h-1) ln x / (1)
= x^0 ln x / 1
= 1 * ln x
= ln x