Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.9 AIME Find the answer

7. Given $0<x<1$ , and $\log _{2} x=\log _{3} y$ $=\log _{5} z$ , then the order from smallest to largest of $x^{\frac{1}{2}}, y^{\frac{1}{3}}, z^{\frac{1}{8}}$ is $\qquad$ $\cdot$

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

7. $y^{\frac{1}{5}}<x^{\frac{1}{2}}<z^{\frac{1}{5}}$

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