Summand on Entropy

Consider an element of the form \( x_i \log(\frac{1}{x_i}) \), which makes up the sum to calculate entropy. As a function itself, \( f(x) = x \log(\frac{1}{x}) \) has the below shape:

and for a log of base \( b \) the maximum is reached at [\( \;x=\;?\;\)].