Not able to delete lot of files at once in linux
Solution 1:
GNU find has the -delete option, which is always safe:
find . -type -f -delete
As commented elsewhere, you may use xargs too, but be very careful how you use it.
find . -type f -print0 | xargs -0 rm -vf
Solution 2:
All the other answers assume that you want to keep the directories, but it's not clear from your original message that you do; moreover, even if you wanted to keep the structure, you'll need to remove and recreate the directories anyway, because the directory files have become very large - they won't shrink when you empty them, and their size will massively slow down operations in them in future.
So have you considered just
rm -rf log*
Solution 3:
If you can manage the many errors when rm fails to delete directories, you can approach the problem from the other side
for dir in $(find . -type d)
do
rm $dir/*
done