2002 #17 and 25

Using every possible rule of Logarithms and a bit of combinatorial thinking:

Difficulty: Pretty Tough for students.

Difficulty: Much simpler than it appears. Brute force solution works best.

Standard instructions for this series: No calculator allowed. Express  answers in reduced form. Rationalize denominators. Radicals must be  reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 17 and answer 25.