solving for a variable that exist inside as well as outside of natural log or exponent

Question

can the following equation be solved for K analytically? If not, then what other approaches I could try out?

K*ln[(C2-K)/(C1-K)] = -(F/V)*t

The original equation was:

C2 = K + (C1-K)*exp(-(F/KV)*t)

Answer 1

To start, I point out a few things.

A) You could simply solve for $K$ using Lagrange Inversion Theorem.

B) You could try to solve for $K$ in closed form using the Lambert W function.

As for A), you will need to understand calculus.

As for B), I know it won't work, it only works to solve some problems of this type.

I can solve the following:

$$K\ln(K)=A$$

$$K^K=e^A$$

$$K=e^{W(A)}$$

Solution here. However, a problem like:

$$K\ln(K+a)=A$$

Is unsolvable.

Yours is also unsolvable.