Well, you actually gotta take then exists so that
On the other hand is so and then so pick the second inequality and
Using the Mean Value Theorem, prove that ln(103) - ln(100) is less than or equal to 0.03
I tried taking f(x) = 1/x on the interval [100,103]. The average value would then be (1/3)[ln(103)-ln(100)].
I don't know how to proceed after this or even if I'm on the right track.