How to solve equation that contain additive in exponent? $$
\begin{align}
\text{I have equation : } & \left(\frac{y_2+c}{y_0+c}\right)^p=\frac{y_1+c}{y_0+c} & \text{find : } c \text{ when } y_n \text{ is constant}
\\
\text{Or in another form : } & \left(\frac{x+a}{x+c}\right)^p=\frac{x+b}{x+c}  &   \text{find : } x \text{ when } a,b,c,d \text{ is constant}
\end{align}
$$
Where p is any real number and c is any real number which $x + c > 0$, Can this equation be solved?
On the other hand what I actually did is try to reverse below equation with systems of equation
$$y = ax^b - c$$
Given 3 points of $(x,y)$ that following each other in monotonic fashion should be able to solve this equation, so far I could derived a new equation like so https://www.desmos.com/calculator/ydkxrhdplq
This below image is result I try to made, find $a$ $b$ and $c$ to make this equation pass this 3 points. The problem is I can't find equation for solving $c$ and need to guess it as constant
Or what I try to do is actually not possible?


To approach a solution, try to logarithmize on both sides of the equation, i.e.
$$ \log \left(\frac{x+a}{x+c}\right)^p \; = \; \log \frac{x+b}{x+c}$$
In order to simplify the left side: What do you know about $\log y^z$?
