You can do this with extended pattern matching in bash, e.g.
> shopt -s extglob
> ls *'.'+([0-9])
Where
+(pattern-list)
Matches one or more occurrences of the given patterns
And other useful syntaxes.
?(pattern-list)
Matches zero or one occurrence of the given patterns
*(pattern-list)
Matches zero or more occurrences of the given patterns
@(pattern-list)
Matches one of the given patterns
!(pattern-list)
Matches anything except one of the given patterns
Alternatively without extended pattern matching could use a less neat solution
ls *'.'{1..1000} 2>dev/null
And replace 1000 with some larger number if you have a lot of log files. Though I would prefer the grep option to this one.