In the context of machine learning deep learning, what does a "log space" mean?

Question

ch06 of "deeplearningbook" says

This approach to predicting the probabilities in log space is natural to use with maximum likelihood learning.

"log space" also appears a lot of times in math.stackexchange.com.

so, what is "log space", In the context of machine learning deep learning?

does "log space" mean put a log on any function?

I googled it and the most likely result linked to L (complexity) without any explanation about Logarithmic space.