If f(x)=ekxf(x) = e^{kx}f(x)=ekx and f(n)(x)f^{(n)}(x)f(n)(x) denotes the nnn-th derivative, for what value of kkk is f(n)(0)=2nf^{(n)}(0) = 2^nf(n)(0)=2n for all nnn?
k=1k = 1k=1
k=ln2k = \ln 2k=ln2
k=2k = 2k=2
k=ek = ek=e