# Solving complicated logarithmic equation symbolically

For a research application, I am trying to solve this system for the variable $$c$$. I have tried WolframAlpha and Sympy to no avail, so I was wondering if there was a program or tool that would be able to solve this. Maybe a Taylor expansion is the best approach?

$$\begin{equation*} \frac{m + d(-ln(1 - a^{3}(c+f)))}{q + r(-ln(1 - a^{3}(c+f)))} - c = 0 \end{equation*}$$

The Sympy code I tried was

import sympy as sym

m,d,a,c,f,q,r = sym.symbols('m d a c f q r')
RHS = c
LHS = (m+d*(-sym.log(1-a**3*(c+f)))) / (q+r*(-sym.log(1-a**3*(c+f))))
result_of_it = sym.solve(LHS-RHS, c)
print(result_of_it)

• By "complex equation", do you mean an equation $\in \Bbb C$, or a complicated/difficult equation? If it is the latter, please remove the complex, as it is misleading. – Rhys Hughes Oct 25 '18 at 0:04
• @RhysHughes resolved – kdissel Oct 25 '18 at 0:06
• Since $c$ is both inside and outside the logarithms, the equation is transcendental. The value of $c$ can only be approximated with numerical methods. – Blue Oct 25 '18 at 0:18
• If $c$ is suppose to be "small", a series expansion could give an approximation. – Claude Leibovici Oct 25 '18 at 4:21