As the console log is not so easy to read, you could try the System Report/Extensions? Mine currently reads the following (from the detail as I couldn't copy the list view) (and note the "Loaded"):
ATI2600Controller:
Version: 1.6.6
Last Modified: 24/10/2013 18:09
Loaded: No
Get Info String: ATI2600Controller 1.6.6.25 (7429)
Obtained from: Unknown
Kind: Intel
Architectures: i386, x86_64
64-Bit (Intel): Yes
Location: /System/Library/Extensions/ATI2600Controller.kext
Kext Version: 6.0.6
Valid: Yes
Authentic: Yes
Dependencies: Satisfied
Signed by: Unknown
ATIFramebuffer:
Version: 1.6.6
Last Modified: 24/10/2013 18:09
Loaded: No
Get Info String: ATIFramebuffer 1.6.6.25 (7429)
Obtained from: Unknown
Kind: Intel
Architectures: i386, x86_64
64-Bit (Intel): Yes
Location: /System/Library/Extensions/ATIFramebuffer.kext
Kext Version: 6.0.6
Valid: Yes
Authentic: Yes
Dependencies: Satisfied
Signed by: Unknown
ATIRadeonX2000:
Version: 8.18.27
Last Modified: 20/09/2013 07:06
Loaded: Yes
Get Info String: ATIRadeonX2000 8.18.27 12975
Obtained from: Apple
Kind: Intel
Architectures: x86_64
64-Bit (Intel): Yes
Location: /System/Library/Extensions/ATIRadeonX2000.kext
Kext Version: 8.1.8
Load Address: 18446743521831400000
Valid: Yes
Authentic: Yes
Dependencies: Satisfied
Signed by: Software Signing, Apple Code Signing Certification Authority, Apple Root CA
ATISupport:
Version: 1.6.6
Last Modified: 24/10/2013 18:09
Loaded: Yes
Get Info String: ATISupport 1.6.6.25 (7429)
Obtained from: Unknown
Kind: Intel
Architectures: i386, x86_64
64-Bit (Intel): Yes
Location: /System/Library/Extensions/ATISupport.kext
Kext Version: 6.0.6
Load Address: 18446743521843300000
Valid: Yes
Authentic: Yes
Dependencies: Satisfied
Signed by: Unknown
and for the AMD Extensions:
AMD2400Controller:
Version: 1.14.21
Last Modified: 20/09/2013 06:26
Loaded: No
Get Info String: AMD2400Controller 1.14.21 12975
Obtained from: Apple
Kind: Intel
Architectures: x86_64
64-Bit (Intel): Yes
Location: /System/Library/Extensions/AMD2400Controller.kext
Kext Version: 1.1.4
Valid: Yes
Authentic: Yes
Dependencies: Satisfied
Signed by: Software Signing, Apple Code Signing Certification Authority, Apple Root CA
AMD2600Controller:
Version: 1.14.21
Last Modified: 20/09/2013 06:26
Loaded: Yes
Get Info String: AMD2600Controller 1.14.21 12975
Obtained from: Apple
Kind: Intel
Architectures: x86_64
64-Bit (Intel): Yes
Location: /System/Library/Extensions/AMD2600Controller.kext
Kext Version: 1.1.4
Load Address: 18446743521841300000
Valid: Yes
Authentic: Yes
Dependencies: Satisfied
Signed by: Software Signing, Apple Code Signing Certification Authority, Apple Root CA
AMD3800Controller:
Version: 1.14.21
Last Modified: 20/09/2013 06:26
Loaded: No
Get Info String: AMD3800Controller 1.14.21 12975
Obtained from: Apple
Kind: Intel
Architectures: x86_64
64-Bit (Intel): Yes
Location: /System/Library/Extensions/AMD3800Controller.kext
Kext Version: 1.1.4
Valid: Yes
Authentic: Yes
Dependencies: Satisfied
Signed by: Software Signing, Apple Code Signing Certification Authority, Apple Root CA
AMD4600Controller:
Version: 1.14.21
Last Modified: 20/09/2013 06:26
Loaded: No
Get Info String: AMD4600Controller 1.14.21 12975
Obtained from: Apple
Kind: Intel
Architectures: x86_64
64-Bit (Intel): Yes
Location: /System/Library/Extensions/AMD4600Controller.kext
Kext Version: 1.1.4
Valid: Yes
Authentic: Yes
Dependencies: Satisfied
Signed by: Software Signing, Apple Code Signing Certification Authority, Apple Root CA
AMD4800Controller:
Version: 1.14.21
Last Modified: 20/09/2013 06:26
Loaded: No
Get Info String: AMD4800Controller 1.14.21 12975
Obtained from: Apple
Kind: Intel
Architectures: x86_64
64-Bit (Intel): Yes
Location: /System/Library/Extensions/AMD4800Controller.kext
Kext Version: 1.1.4
Valid: Yes
Authentic: Yes
Dependencies: Satisfied
Signed by: Software Signing, Apple Code Signing Certification Authority, Apple Root CA
AMD5000Controller:
Version: 1.14.21
Last Modified: 20/09/2013 06:26
Loaded: No
Get Info String: AMD5000Controller 1.14.21 12975
Obtained from: Apple
Kind: Intel
Architectures: x86_64
64-Bit (Intel): Yes
Location: /System/Library/Extensions/AMD5000Controller.kext
Kext Version: 1.1.4
Valid: Yes
Authentic: Yes
Dependencies: Satisfied
Signed by: Software Signing, Apple Code Signing Certification Authority, Apple Root CA
AMD6000Controller:
Version: 1.14.21
Last Modified: 20/09/2013 06:26
Loaded: No
Get Info String: AMD6000Controller 1.14.21 12975
Obtained from: Apple
Kind: Intel
Architectures: x86_64
64-Bit (Intel): Yes
Location: /System/Library/Extensions/AMD6000Controller.kext
Kext Version: 1.1.4
Valid: Yes
Authentic: Yes
Dependencies: Satisfied
Signed by: Software Signing, Apple Code Signing Certification Authority, Apple Root CA
AMD7000Controller:
Version: 1.14.21
Last Modified: 20/09/2013 06:26
Loaded: No
Get Info String: AMD7000Controller 1.14.21 12975
Obtained from: Apple
Kind: Intel
Architectures: x86_64
64-Bit (Intel): Yes
Location: /System/Library/Extensions/AMD7000Controller.kext
Kext Version: 1.1.4
Valid: Yes
Authentic: Yes
Dependencies: Satisfied
Signed by: Software Signing, Apple Code Signing Certification Authority, Apple Root CA
AMDFramebuffer:
Version: 1.14.21
Last Modified: 20/09/2013 06:26
Loaded: Yes
Get Info String: AMDFramebuffer 1.14.21 12975
Obtained from: Apple
Kind: Intel
Architectures: x86_64
64-Bit (Intel): Yes
Location: /System/Library/Extensions/AMDFramebuffer.kext
Kext Version: 1.1.4
Load Address: 18446743521841200000
Valid: Yes
Authentic: Yes
Dependencies: Satisfied
Signed by: Software Signing, Apple Code Signing Certification Authority, Apple Root CA
AMDRadeonX3000:
Version: 1.14.21
Last Modified: 20/09/2013 06:26
Loaded: No
Get Info String: AMDRadeonX3000 1.14.21 12975
Obtained from: Apple
Kind: Intel
Architectures: x86_64
64-Bit (Intel): Yes
Location: /System/Library/Extensions/AMDRadeonX3000.kext
Kext Version: 1.1.4
Valid: Yes
Authentic: Yes
Dependencies: Satisfied
Signed by: Software Signing, Apple Code Signing Certification Authority, Apple Root CA
AMDRadeonX4000:
Version: 1.14.21
Last Modified: 20/09/2013 06:26
Loaded: No
Get Info String: AMDRadeonX4000 1.14.21 12975
Obtained from: Apple
Kind: Intel
Architectures: x86_64
64-Bit (Intel): Yes
Location: /System/Library/Extensions/AMDRadeonX4000.kext
Kext Version: 1.1.4
Valid: Yes
Authentic: Yes
Dependencies: Satisfied
Signed by: Software Signing, Apple Code Signing Certification Authority, Apple Root CA
AMDSupport:
Version: 1.14.21
Last Modified: 20/09/2013 06:26
Loaded: Yes
Get Info String: AMDSupport 1.14.21 12975
Obtained from: Apple
Kind: Intel
Architectures: x86_64
64-Bit (Intel): Yes
Location: /System/Library/Extensions/AMDSupport.kext
Kext Version: 1.1.4
Load Address: 18446743521840700000
Valid: Yes
Authentic: Yes
Dependencies: Satisfied
Signed by: Software Signing, Apple Code Signing Certification Authority, Apple Root CA
But have also seen at least one other report that after a Mavericks freeze just the repair permissions appeared sufficient. Probably all too early to tell, but my ATI2600 froze within a day, so have done the kext + repair permissions - but it is has only been running for just under a day so far. (I thought it was a subtle hardware issue between batches of cards, but the fact that it spans multiple gpu cards but not every machine makes it a very bizarre issue - and I understand Apple do not formally monitor these posts, they just kindly host them. Do a bug report to Apple, I did, but after sending several crash logs they eventually asked me to take it to a store, but I could not be bothered. If everyone reported a bug they might look a little deeper ~ but these machines are well out of warranty now, unless other newer ones are also having issues)