Adjacency-list to Adjacency matrix in logarithmic space?
Any time you have a problem parameterized by a number&nbsp;$n$ and you need an algorithm whose space usage is logarithmic in&nbsp;$n$, you should immediately think "loop counter". You can store numbers in the range $0$&ndash;$n$ in $\Theta(\log n)$ bits.

So, in this case, you can use an algorithm along the lines of

for i = 1 to n
    for j = 1 to n
        if j is in i's adjacency list
            write 1 to the output
        else
            write 0 to the output


The loop counters take $\log n$ bits each, and you might need a small amount of extra storage for book-keeping but you only need to store a constant number of data items, and none of those will be anything bigger than a number in the range $0$&ndash;$n$, so that's still only $O(\log n)$.