Except checking whether the folder is empty or not, i would also like to know whether the *.log files are removed. Here is another example.

#!/bin/sh
# Read a folder path from user input and check if
# there is any .log file

# Read the folder location
# "\c" means keep the cursor on the same line
echo "Please input the folder location: \c"
read _folder

# Quit if the folder does not exist
if [ ! -e $_folder ]; then
        echo 'Sorry, folder does not exist.'
        exit 1
fi

# Check if the folder contains any .log files
if [ -z "$(find $_folder -name \*.log -print)" ]; then
        echo "$_folder does not have any log files"
else
        echo "$_folder contains log files"
fi

Done =)