Sketch an image under w = \text{Log} (z) of

i) the line y=x
ii) the line x=e


I have not done many problems with mappings under the principal value mapping of the logarithm. I know that

\text{Log} (z) := \ln r + i \theta = \ln | z | + i \text{Arg} (z).

However, I do not see what these images would look like. I need a few pointers here on what to do.