Inequalities - Math Central

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Quandaries & Queries

Question from Sindhu, a student:

prove that

4^79 < ( (2^100) + (3^100) )< 4^80?

Hints:
(1) How does 2¹⁰⁰ compare with 3¹⁰⁰?
(2) Write 4⁷⁹ and 4⁸⁰ as powers of 2.
(3) What is log(3)/log(2)?

Good Hunting!
RD

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