There is already a log for camping nights, service hours, and miles hiked. The National Outdoor Badge for Aquatics, Adventure, and Riding also have similar things that need to be done that would be easier if there was a log.
For aquatics, there could be an “One-the-water” log or simply “Aquatics” log that tracks the number of hours a Scout has spent doing aquatic activities. For riding, there could be a “Riding” log that tracks the miles of riding activities.
And for adventure, there could be an “Adventures” log that tracks the number and type of adventures of a certain activity. For example, a 12-day Philmont trek, covering at least 80 miles would have 4 adventures from the time/mileage requirement, 1 adventure from it being at a high adventure base, and 1 adventure from the 50-miler award (assuming it is earned) for a total of 6 adventures. So, the log would have to have an option to mark 4 adventures for time/mileage, 1 for high adventure base, and 1 for 50-miler.