Non-Linear Model Transformation

Question

I want to transform this Non-Linear Model $y= 8-ae^{bx}$ to Linear.And my issue is in this step $lny=ln(8-ae^{bx})$ how can simplify it to reach in a linear model which is like this $y*=b0+b1x$

while in the classic problem $y=ae^{bx}$ we are tansforming like this $lny=ln(ae^{bx})$ $<=>$$lny = lna+ln(e^{bx}$) $<=>$ $lny=lna +bx$ , where $y*=lny$, $lna=b0$ and $b=b1$ thus we got $y*=b0+b1x$

Answer 1

$8-y = ae^{bx} \to \ln (8-y)=\ln a + bx$, if $8-y_{i}$ is not strictly larger than $0$ for all $y_{i}$, then you can add some constant $c$ to ensure it. It won't effect the ANOVA analysis, but you should account for this additive term when you draw conclusions regarding the values of the dependent variables.