time complexity - When can a quadratic algorithm be better than an logarithmic one?

Question

As in when there are two algorithms that solve the same problem, one being quadratic and one being logarithmic, what context would mean it would be preferable to use the quadratic one, despite the implicit detriments.

Answer 1

A quadratic algorithm can be better up to a certain point, if the logarithmic one has a significantly larger constant, for example: first algorithm performs 1000 * logN operations (exactly - for simplicity), and another one - 3 * N^2. Then, up to about N = 20, the quadratic algorithm will perform better.