By default, the ASPNET user does not have permissions to write to default event logs---even the Application log. One way to address this issue is to let your web application impersonate a user with the correct permissions by entering the impersonate element in the system.web element of the Web.config file:
<system.web>
...
<identity impersonate="true" userName="MyUserName" password="MyClearTextPassword" />
...
</system.web>
Another way is to use the Security > Permissions... command in regedt32 on this key:
HKEY_LOCAL_MACHINE\\System\\CurrentControlSet\\Services\\EventLog
Add the ASPNET account and grant Full Control.