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

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The equation involves an unknown constant equal to a known value plus the logarithm of another unknown. It is noted that if the unknown appears both inside and outside the logarithm, it cannot be solved using elementary functions. The discussion suggests that the solution may be possible using the Lambert W function, which is the inverse of the function f(x) = xe^x. This approach indicates a non-trivial solution exists, but it requires advanced mathematical concepts. Understanding the Lambert W function is essential for solving this type of equation.
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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.
 

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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.
 

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