bsically if we have an estimation for Chebyshev constant with:
pi(x) < C x/ln x
then pi(x) * ln x < C * x => x^pi(x) < (e^C)^x.
So we need to show 2*ln2 = 1.38629436+ is a good Chebyshev constant. Actually, there are proofs that 1.256 is a good Chebyshev constant.