Neil one thing...
The formel to the arc line

see
http://mathworld.wolfram.com/LogarithmicSpiral.html part (6)
And from that formel the arc length measured from the origin
So schould it not be
[a*e^(b*THETA)*(1+b^2)^(1/2)]/b-[a*e^(b*ZERO)*(1+b^2)^(1/2)]/b=300 and then we find Theta..
I this case I get theta to 15,129
Because we walk from Theta=0 to theta=arc line 3000 m