I just started working on the Black Scholes formula with help of the book Financial option valuation by Higham. Apparently you are possible to derive the following function:
$\log(\frac{SN'(d_1)}{e^{-r(T-t)}EN'(d_2)}) = 0$
From the Black scholes formula:
$C(S,t)=SN(d_1)-Ee^{-r(T-t)}N(d_2)$
I've been puzzling arround but I'm stuck. This is where I came so far, do you know where I'm going wrong?
$\log(\frac{SN'(d_1)}{e^{-r(T-t)}EN'(d_2)}) = \log(SN'(d_1))-\log(e^{-r(T-t)}EN'(d_2))=0$