Missing digit of two to the 29th

The number $2^{29}$ has nine digits, all different. Which digit from $0$ to $9$ does not appear in it? Try to find it without computing $2^{29}$ fully.

$4$. A number is congruent to its digit sum mod $9$. Since $2^6\equiv1$, $2^{29}\equiv2^5\equiv5 \pmod 9$, while the digit sum is $45-x\equiv -x$. So $x\equiv4$, and indeed $2^{29}=536870912$.