I have been using tools such as WolframAlpha to solve a series of equations. I've recently come across an equation which the computers seemingly aren't able to solve. I'd like to know what about this equation makes it unsolveable by computers and what the answer is if one exists.
I'm attempting to solve $$AB+1=B^C$$ for B. How can B be written as a function of A and C?
Best Answer
There is no analytical solution to finding $B$. However, you can rewrite the equation as $f(B)=B^C-AB-1=0$. After that, we note that the derivative with respect to $B$ is $f'(B)=CB^{C-1}-A$. Therefore, we can use Newton's method to calculate $B$, and we have $$B_{n+1}=B_n-\frac{B_n^C-AB-1}{CB_n^{C-1}-A}$$ This is an example of using a spreadsheet to get B.