It could be unwritable if the folder is owned by your userID, and PHP (which has a different userID) is trying to create a new file in it.
The folder being unwritable means that PHP can't create a new file there, but it is still possible to manually create a file in that folder that *can* be written to by PHP:
Use your control panel's File Manager to manually create the file
/logs/error.log
The file will be owned by your userID.
In File Manager, set the permissions of the error.log file to 666 (rw-rw-rw-). This makes it possible for PHP to write data into the file.
It is a minor security risk because it has the side effect of allowing all the other userID's on your shared server to write to it, too, but shared servers are not typically full of malicious users who would do that. A malicious script in a hacked website on the server could also write to the file, but, again, that is not a rampant scenario.
With the PHP configuration that you seem to have, this is the only way to allow PHP (or Apache) to write to a file that your userID owns.
A small amount of protection would be to name the file something more complicated and less obvious than "error.log".