observations 1,2,...n are made from a distribution with the following pdf:
f(x)=theta/x^(theta+1)
find an expression for theta hat.
Starting from the definition of the liklihood function, you end up with $\displaystyle \frac{\theta ^ n}{\prod _{i = 1} ^ n x_i ^ {\theta + 1}}$. From there, the trick should be to maximize the log of this guy, which is a pretty standard thing to do. In most cases, maximizing a function is equivalent to maximizing its log. I ended up with $\displaystyle \hat{\theta} = \frac{n}{\sum _ {i = 1} ^ n \mbox{log}(x_i)}$ if I did it right.