AIME 2015 Problem 4

Geometry Level 3

In an isosceles trapezoid, the parallel bases have lengths \(\log 3\) and \(\log 192\), and the altitude to these bases has length \(\log 16\). The perimeter of the trapezoid can be written in the form \(\log 2^p 3^q\), where \(p\) and \(q\) are positive integers. Find \(p + q\).


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