Can we update error.log format in kong

Hi ,

i am using kong 2.0.3 version with db-less mode. i wanted to put kong logs into centralised logging framework. so i am using correlation id plugin to get trace_id for each call. and also i updated access.log format of kong to include the trace_id in it by using below changes in nginx_kong.lua file

log_format custom_log_format ‘$remote_addr - $remote_user [$time_local] “$request” $status $body_bytes_sent “$http_referer” "$http_traceId" “$http_user_agent” “$http_x_forwarded_for”’;

access_log ${{PROXY_ACCESS_LOG}} custom_log_format;

can anyone tell me, is der any way i can update error.log also with trace_id?
becasue as per documentation error.log can be adjusted by log_level