It will be in the folder where X1 keeps its index.
In my case it is here:
E:\Data\X1\Search 8\X1 Search\logs
But I have moved the index so for most people try:
C:\Users\{username}\AppData\Local\X1 Search\logs%userdata%
Or
%LOCALAPPDATA%\X1 Search\logs
Paste that into the location slot in Windows Explorer and see where it takes you.
In my case it is here:
E:\Data\X1\Search 8\X1 Search\logs
But I have moved the index so for most people try:
C:\Users\{username}\AppData\Local\X1 Search\logs%userdata%
Or
%LOCALAPPDATA%\X1 Search\logs
Paste that into the location slot in Windows Explorer and see where it takes you.