why output values of linear transformation are wrong?

Question

I am going to fit my data using an equation, Y=a*(1-e^(-bx))^c equation. a & c are the intercept and slope, b is given.

Here are the steps I did:

1. I transformed Y=a*(1-e^(-bx))^c equation into log(Y)=log(a)+c*log(1-e^(-bx))
2. solved intercept and slope: 
   log(a)+c =log(Y)/log(1-e^(-0.3*x) (b=0.3)
3. fitted linear model log(a)+c VS log(x)
4. extracted intercept and slope: a=5.19 & c=-2.15 
5. replaced them into original equation like this. 
   Y=5.19*(1-e^(-0.3)*x))^(-2.51). 

Here is main issue, when I use this equation for my data, output gives me wrong values. So can you check the steps whether they are right or not? It seems right, but....

Thank you in advance!

Answer 1

If so, then we get $$\log(y)=\log(a)+c\log(1-e^{-bx})$$

Answer 2

1. Transform $Y=a(1-e^{-bx})^c$ equation into $\log(Y)=\log(a)+c\log(1-e^{-bx})$ assuming both $Y$ and $1-\exp(-bx)$ are both positive.

2. Fit linear model $\log(Y)$ againts $\log(1-e^{-bx})$ since $b$ has been given to you. $\log(a)$ is the intercept and $c$ is the slope.

3. compute $a$ to be exponential of the intercept and $c$ is the slope and plot the original graph using these values.