Is there any way to resize the log window?

[Jeeqbit]

You can resize the log window, yes. At the top and to the right there are a few lines and you can click and drag it to resize it. I don't think this affects the size of the bar below it with all the tabs, but you can rename the tabs to have smaller names. You can change the chat prompt's font size in the log window settings as well. There is a button at the bottom of the chatbox to get to these settings.