Solving for $x$ in discrete logarithm
Solution 1:
We check by hand and get $2^{6} \equiv 9 \pmod{11}.$
By Fermat's little theorem, $2^{10} \equiv 1 \pmod{11}.$
$2^{10n+6}\equiv 2^{6} (2^{10})^{n}\equiv2^{6}\equiv9 \pmod{11}.$
Hence $x=10n+6$ for all $n\in\Bbb Z.$