Some file types support more than 1 extension, for example jpe, jpeg, jpg, etc. for jpeg files.
What you can do is get the mime type first:
mimleType=$(awk -F';' 'NF>1{print $1}' < <(file -bi logo.jpeg))
Then use this awk to get the file extension:
awk -v mt=$mimeType '$1==mt{print $2}' /Applications/MAMP/conf/apache/mime.types
OUTPUT:
jpeg
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