How to show MULT={a#b#c| a,b,c binary natural numbers and a ✕ b = c} is in Log Space?
In high-school multiplication, you multiply $a$ by $b$ by summing shifted copies of $b$, some of them zeroed out (according to $a$). You can implement this algorithm in logspace by calculating the result from LSB to MSB, keeping track of the carry. The crucial point is that the carry is only $O(\log n)$ bits long.