Is e^x=ln(x) solvable?

We will solve an interesting algebraic equation involving both exponential and logarithm, namely e^x=ln(x). Although the graphs of y=e^x and y=ln(x) do not intercept, we can actually find some complex solutions to this equation. We do need to use the Lambert W function tho. So see here for a detailed lecture. Lambert W function Lecture:    • Lambert W Function (domain, range, ap...  
We will make b^x and log_b(x) tangent to each other here:    • the famous equation b^x=log_b(x)  

Check out Mu Prime Math's video on when is f(x)=f^-1(x)=x true:    • When does f(x)=f⁻¹(x) mean f(x)=x? - ...  
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