Here is the general rule
$Given\ b,\ c > 0\ and\ b \ne 1: a = log_b(c) \iff c = b^a.$ This is a definition and needs to be memorized.
So, as Romsek has already explained, $9x = log_6(d) \implies d = 6^{9x}.$
The only tricky thing is that sometimes the base of the logarithm is implied.