The one-way function for Diffie-Hellman
Modular exponentiation: Given a prime p, and numbers a and w less than p, compute y=aw modulo p. (Can be done in log2w steps.)
Discrete log problem: Given p, a, and y, find a w such that y=aw modulo p. (Requires time on the order of p as far as anyone knows.)
So if we take p to be a 500 digit prime, the difference between the computing effort to compute powers mod p versus computing discrete logs mod p is on the order of 2500