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\frac{3}{2}-\log_{27}\left(9\right)
The base 9 logarithm of 27 is \frac{3}{2}.
\frac{3}{2}-\frac{2}{3}
The base 27 logarithm of 9 is \frac{2}{3}.
\frac{5}{6}
Subtract \frac{2}{3} from \frac{3}{2} to get \frac{5}{6}.