The point is that "e^x" is the inverse function to "ln(x)". That is, and . You "introduce the e" (by which I assume you mean "take the exponential of both sides") When you have ln of something on one side and want to get rid of the ln.
(Again, what you wrote, "Lo(1_e^hw)", makes no sense. Did you mean " "?)
Here is the equation I have been asked to solve for L.
I would insert an image but for some reason I am not able to. So I have attached the image to this post. I had an existing equation that I had done before, but I had to work backwards.
I know I went wrong somewhere (You're right, I don't think the 'e' was required).