Some things in the challenge log you can't help but complete while leveling, such as dungeon roulette.
Other items require you to go a bit more out of your way, such as 10 unique FATEs, and FATEs from 5 different zones; as well as 5 and 20 levequests.
The xp awarded for completing these criteria is far too low; it comes out to roughly 6% per challenge log (4% for the lesser bonuses) of your xp bar, but it's for the week. That ends up at <1% of your xp bar per day.
Compare that to the bonuses for using the daily roulette, which combined offer roughly 65% for pre 53, and around 30% from 53-60. That's every day.
These challenge log bonuses should boosted to at least 5x their current value, as they can only be obtained once per week; and the bonus would still be roughly half that of the roulette bonuses obtainable every day. Personally, I think they should be boosted to 10x their current value; and doing them each week would be like cramming in an extra day of duty roulettes at the end of the week.
Currently, these challenge log bonuses are so small that often it's not worth breaking away from a FATE party in a relevant zone to obtain them. Aside from the dungeon log bonuses, which will be gained anyway as daily roulette bonuses are collected, it's ultimately less xp per hour to fulfill the challenge log criteria that grant an xp reward compared to dungeon grinding (for tanks and healers) and FATE grinding.
For a game that encourages replaying the 1-60 leveling phase multiple times, most the avenues for bonus xp are underwhelming; and efficient means for leveling have a severe diversity problem.