Symbolic Expansion

Working with logarithms. I was wondering why the symbolic engine will not "expand" out the variables? Am I doing something wrong?

You are making a very common mistake. When doing algebraic manipulations people frequently make implicit assumptions about the domain of the variables, but Mathcad's symbolic engine (especially the MuPad engine in MC14 and later) does not.

Also, I would like to work symbolically upfront. In the attached, I want to expand/combine/simplify in terms of log symbolically. I then want to set that result to a variable, L. This way I can "prove the math" before applying values to the variables. Problem that I have is that as soon as I assign "L" to the symbolics, it wants a value. If I modify, the symbolics, I have to "cut & paste" into a variable definition.

Make L a functoin of the undefined valiables, just as you would in a purely numeric function defintion.