Anyone able to identify tree fungus?

[BabelFishy]

I've noticed two patches of fungus on one mature eucalyptus tree in my garden. Does anyone know what they are and whether they will damage the tree?

The flat looking one is at head height and the knobbly one (with ivy in the photo) is at the base.

Cheeky bump in case any evening experts about...

The first one might be Trametes, possibly Trametes hirsuta. The second one - no idea.

I think you might be on the money there with trametes, thank you!!