Comparing two symbolic expressions

Question

Does Mathematica provide any way to compare two symbolic expressions and find which is the greatest? For example, I want to find which is the greatest of (n - 1) + 2(n - 1) Log[2, n] or n(n - 1)/2, where n is a variable.

Answer 1

Reduce[(n - 1) + 2 (n - 1) Log2[n] > n (n - 1)/2, n, Reals]

Returns that the statement is true for $$0 < n < \frac{-4}{\ln 2} \text{ProductLog}(\frac{-\ln 2}{4 \sqrt{2}})\lor 1 < n < \frac{-4}{\ln 2}\text{ProductLog}(\frac{-\ln 2}{4 \sqrt{2}})^*$$ Where $\text{ProductLog}$ is the solution to the Lambert W equation. As @Rojo notes in the comments, use N to find a numerical approximation.

General note: try using the free-form input in MMA to get a primary understanding for individual functions themselves and to learn of knew ones, such as Reduce.