Suppose that $n, k, b \in \mathbf{N^\ast}$ are constants, $C \in \mathbf{R}_{>0}$ is also a constant, and that $f(n,k,b,j)$ and $g(n,k,j)$ are real valued functions.
Is there an algebraic way to solve $$\sum_{j=0}^{b-1} f(n, k, b, j) \cdot g(n, k, j)^x = C$$ for $x$, or only numerical methods can be used?