With kernel 2.6.18, the maximum size of a bootable partition (the root) is 2 TB. However since lv_log is not a bootable partition, I would assume it can be at least 4TB. Could even be up to 32TB depending on the block size, see ext3 - Wikipedia
To determine the block size, run this: tune2fs -l /dev/mapper/vg_splat-lv_log | grep -i 'block size'
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