I was curious, I installed a bitnami stack with php 7 rc5, it's wamp on windows 10 and of course apache. Laravel ver is 5.1.11, all is working fine on this setup. So it has to be a Nginx problen I'm guessing. Please keep us informed. My other answer was a previous ver of laravel.
I had the same error, with PHP 7 on my Window Machine, but the same code ran fine on my Ubuntu 14.x.
What I found was mbstring was not enabled in my PHP.ini on the Windows PHP 7 install.
Class log does not exist
it Means Your Missing a Vendor File
The Fixed For That is Completely Remove Vendor file
But Make Sure Your Composer.lock is Present
Then Run Composer Install It Should Re Install All Missing File in Your Vendor File
The error output is too confusing to be related with an extension. But after install PDO extension on my PHP 7, there's no error anymore. Hope it helps:)