It's a tough question... there are lots of threads about battery life. If you use it for three solid hours of actual continuous internet surfing, especially while listening to the iPod function, or game playing, yes, it will draw down on battery life significantly. Three hours of usage mixed between the phone and the web seems slightly low to me.
Another thing though is that a lot of us used our phones tons during the first month -- more than we realized and more than we did afterwards. In my first month, I never had to charge it twice a day, but it would often be close to dead at the end of the day. Now I use it as much as I want, and it almost never gets to the red line by the end of the day, even when I spent 2+ hours on train rides using the iPod continuously and a fair amount of web surfing.