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logarithmic inequality involving only primes

Source: Romanian District Olympiad 2002, Grade X, Problem 3

October 7, 2018
number theorylogarithmsinequalities

Problem Statement

Let be two real numbers a,b, a,b, that satisfy 3a+13b=17a 3^a+13^b=17^a and 5a+7b=11b. 5^a+7^b=11^b. Show that a<b. a<b.
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