Caching by avast is, as you might expect, a far greater activity than is logging.
I have never concerned myself with the logging activity - it being, by far, less than caching. For different reasons than yours I asked the avast team some years ago to provide a way to change the caching location from the standard windows system defined temporary disk space location.
As a (then) new arrival in this forum I was most impressed and very pleased when they accommodated my request by providing a registry override for the temporary avast files.
You too may can use this option by creating a new registry key in:
HKLM\SOFTWARE\ALWIL_Software\Avast\4.0
The name of the new key is:
Avast4TempFolder
and in this key you would enter the location of the folder you want avast to use. Mine - for example - is:
F:\TempAvast
Should any of the avast team happen by this post - then I ask (for the reasons I gave before in this forum) that the feature be carried across to the new release of avast being developed.
Others may provide more assistance with the placement of the log files.
Later edit:
I should have made clear that if you have changed the default location of your Windows temporary file placement then avast will have already followed that change for the caching activity. If you have done so then the the use of the avast registry override is not needed.