1. The problem statement, all variables and given/known data In the real linear space C(1, 3) with inner product (f,g) = integral (1 to 3) f(x)g(x)dx, let f(x) = 1/x and show that the constant polynomial g nearest to f is g = (1/2)log3. 2. Relevant equations 3. The attempt at a solution I seem to be able to get g = log 3 but I do not know where the 1/2 comes from. Here is what I did: Let fn = summation (k=0 to n) (f, gk) gk Therefore, (f, gk) = integral (1 to 3) (1/t)(gk)dt and (f, g0) = 0 Hence, (f, g1) = integral (1 to 3) (1/t)dt = log(t) evaluated from 1 to 3 = log (3) - log(1) = log(3) - 0 = log(3). I don't see where the 1/2 comes from or where my mistake is?