I have a very simple solution. I use IntelliJ for development, so the details vary but the idea should apply across all IDE's.
I pick to root of my source tree, right-click and select to do "replace". I then choose to replace all "Log." with "//Log.". This removes all log statements. To put them back later I repeat the same replace but this time as replace all "//Log." with "Log.".
Works just great for me. Just remember to set the replace as case sensitive to avoid accidents such as "Dialog.". For added assurance you can also do the first step with " Log." as the string to search.
Brilliant.