I read somewhere that given two languages $A$ and $B$, if $A \le_{log} B$, then $A \le_P B$ (with $\le_{log}$ the log-space reduction and $\le_P$ the polynomial time reduction), but I'm not sure about the proof.

Could someone help me with that please.

I read somewhere that given two languages $A$ and $B$, if $A \le_{\log} B$, then $A \le_P B$ (with $\le_{\log}$ the log-space reduction and $\le_P$ the polynomial time reduction), but I'm not sure about the proof.

Could someone help me with that please.

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.

I read somewhere that given two languages $A$ and $B$, if $A \le_{log} B$, then $A \le_P B$ (with $\le_{log}$ the log-space reduction and $\le_P$ the polynomial time reduction), but I'm not sure about the proof.

Could someone help me with that please.