1. The problem statement, all variables and given/known data Let f(x) = (1/2+x) log [(1+x)/x] + (3/2-x) log [(1-x)/(2-x)] where log is natural logarithm and 0 < x <= 1/2. Show that f(x) >= 0 for all x. 2. Relevant equations The only inequality that I can think of is the log sum inequality: http://en.wikipedia.org/wiki/Log_sum_inequality 3. The attempt at a solution I try to plot f (see figure), and it seems that the statement is correct. In fact, the figure suggests that f is decreasing and equals 0 at x = 1/2. However, I can't figure out an analytical proof of this.