11/12/2011, 09:56 PM
(11/12/2011, 04:24 PM)Forehead Wrote: As a result,
E^P == TE[x + 1]*P
Now, we rearrange the equation a bit.
Log[E^P] == Log[TE[x + 1]]*Log[P]
I think this is the error. In going from the first to the second equation, it looks like you took, on the right hand side, \( \log(ab) = \log(a) \log(b) \). But that is wrong. Instead, \( \log(ab) = \log(a) + \log(b) \) and so your second equation should be
Log[E^P] == Log[TE[x + 1]] + Log[P]
If we continue your steps with this corrected equation, we get
P == TE[x] + Log[P]
E^P == E^(TE[x] + Log[P])
E^P == E^TE[x] E^Log[P]
E^P == TE[x+1] P
TE[x+1] P == TE[x+1] P
a tautological equation. Though perhaps you could solve for P in the first equation via the Lambert function?
