With ter­abytes of disk­space there is prob­a­bly al­ways some log some­where where stuff shows up:

<4> SysUpTime: 00:00:00 KERNEL Cold restart
<173> SysUpTime: 00:00:12 xDSL linestate up (downstream: 4096 kbit/s, upstream: 512 kbit/s)
<38> SysUpTime: 00:00:13 PPP PAP Authenticate Request sent
<38> SysUpTime: 00:00:13 PPP PAP Authenticate Ack received
<132> SysUpTime: 00:00:13 PPP link up (pppoa_pppoa) [80.126.121.54]

<173> SysUpTime: 01 day 10:19:21 xDSL linestate down
<132> SysUpTime: 01 day 10:19:21 PPP link down (pppoa_pppoa) [80.126.121.54]

<173> SysUpTime: 01 day 10:26:56 xDSL linestate up (downstream: 6304 kbit/s, upstream: 832 kbit/s)
<38> SysUpTime: 01 day 10:27:21 PPP PAP Authenticate Request sent
<38> SysUpTime: 01 day 10:27:22 PPP PAP Authenticate Ack received
<132> SysUpTime: 01 day 10:27:22 PPP link up (pppoa_pppoa) [83.163.219.102]

<132> SysUpTime: 02 days 12:24:37 PPP link down (pppoa_pppoa) [83.163.219.102]

<173> SysUpTime: 02 days 12:24:43 xDSL linestate down
<173> SysUpTime: 02 days 12:25:31 xDSL linestate up (downstream: 4096 kbit/s, upstream: 864 kbit/s)
<38> SysUpTime: 02 days 12:25:59 PPP PAP Authenticate Request sent
<38> SysUpTime: 02 days 12:25:59 PPP PAP Authenticate Ack received
<132> SysUpTime: 02 days 12:25:59 PPP link up (pppoa_pppoa) [83.163.219.102]