Shuffle Deck $7$ times or $8.55$ times?

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Persi Diaconis showed in $1992$ that in order to shuffle a deck of $52$ cards, you need at least $7$ riffle shuffles.

However, in the paper he published, he showed that we needed $\frac{3}{2}\log_2n$ where $n$ is the number of cards in the deck.

$\frac{3}{2}\log_2 52 \approx 8.55$ which is not $7$.

Which answer is right$?$ Should we shuffle $7$ times or $9$ times$?$ I am guessing that the $7$ times comes from a different randomness metric, but I haven't found any article explaining it.

Thank you! :)