From http://wiki.nginx.org/NginxHttpLogModule
[code]
The log file path can contain variables (version >=0.7.4) ..
[/code]

[code] nginx -v
nginx version: nginx/0.7.59[/code]

Config snippet:
[code]
set $client $host;
if ($client ~ "^([a-z0-9]*).admin.mysite.com"){
set $client $1;
}
root /var/www/wordpress/$client/admin;

location / {
...
access_log /var/log/nginx/wordpress/admin/$client/generic-access.log;
error_log /var/log/nginx/wordpress/admin/$client/generic-error.log;
}
[/code]

Fails on test:
[code]
nginx -t
the configuration file /usr/local/nginx/conf/nginx.conf syntax is ok
[emerg]: open() "/var/log/nginx/wordpress/admin/$client/generic-error.log" failed (2: No such file or directory)
configuration file /usr/local/nginx/conf/nginx.conf test failed
[/code]

Have I misunderstood?