After talking with the client I sketched out several different designs based on what we discussed. The client wanted a logo that was simple and reminiscent of a natural sciences sketch. She showed me the image she had already looked at and after a bit of research into the style and animal she wanted depicted, I came up with the designs on the right.
From the designs I sent the client she decided that option 2 and option 4 were her favorites. In my correspondence with her I had asked her to write down anything she didn't like with the designs and let me know. For option 2 she didn't like the flourish at the top and wanted to see the text closer together. For option 4 the client didn't like the design and date coming off the sides.
After making the modifications to the designs that the client asked for, I felt like the designs were then missing something or needed further tweaking. I proceeded to make multiple different variations of the designs and asked again which ones she liked and what she did or didn't like about the design she chose.