How Do You Solve an Equation with Log for an Unknown Constant Plus Unknown?

[likephysics]

Homework Statement

Can you solve an unknown equal to some constant+log of unknown.
please see attached.
All the other variables are known, except Ic1.
How to you solve this?

Homework Equations

The Attempt at a Solution

I have no idea.

 

[HallsofIvy]

If you have $I_{C1}$ both "inside" and "outside" the logarithm, the equation cannot be solved in terms of "elementary" functions. It very likely can be solved, though still non-trivial, in terms of the "Lambert W function" which is defined as the inverse function to $f(x)= xe^x$.