# Relation beetween log-space reduction and polynomial time reduction

I read somewhere that given two languages A and B, if A <=(log) B, then A <=(P) B (with <=(log) the log-space reduction and <=(P) the polynomial time reduction), but I'm not sure about the proof.

Could someone help me with that please.

Thanks.

More generally, $$\mathsf{SPACE}(f(n)) \subseteq \mathsf{TIME}(2^{O(f(n))})$$ for similar reasons. This gives not only $$\mathsf{L} \subseteq \mathsf{P}$$ but also $$\mathsf{PSPACE} \subseteq \mathsf{EXPTIME}$$.