# Help in proving L-Completeness

I'm trying to prove that the following language is L-complete A is a language where each word is comprised of 0s and 1s & the number of 0's is double that of the number of 1's

So far I've managed to show that it can be solved in log space using a counter that adds 2 for every '1' and deducts 1 for every 0.

I need to prove now that every language in L is predictable logarithmically to A

Can't make a comment so have to use an answer. It's a well-known fact that every non-trivial language in $$L$$ is complete under log-space reduction because the reduction could be used to decide the language with only two values for a mapping.