First of all, -mtime 15 brings the files modified exactly 15 days ago. If you want the ones that were modified there is plus 15 days, use -mtime +15.
As for the option -exec, lacked to put a \;:
find -name '*.log*' -mtime 15 -exec rm -f {} \;
Or a +:
find -name '*.log*' -mtime 15 -exec rm -f {} +
The difference is that the first option executes the command rm -f once for each file found, while the second option passes several file names at once to the rm -f, reducing the number of times the control rotates.
Another option is to make one pipe (|) and use the command xargs:
find -name '*.log*' -mtime 15 |xargs rm -f
With that, the exit of find (filenames) are passed as parameters to the command rm -f (similar to the option with + above).
View documentation for more details.
Thank you very much, it worked
– Lucas Marinzeck