8. The number of different shapes of ellipses with eccentricity $e=\log _{p} q$ (where $p, q$ are positive integers not exceeding 9) is

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8. 26 Detailed Explanation: From $0<e<1$ we know $2 \leqslant q<p \leqslant 9$, for $p=3,4,5,6,7,8,9$, the corresponding $e$ values are $1,2,3,4$, $5,6,7$ respectively, totaling 28. However, $\log _{3} 2=\log _{9} 4, \log _{4} 2=\log _{9} 3$, thus there are 26 distinct $e$ values.