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1968 AMC 12 #29 - Ordering Numbers

Source:

January 1, 2012
AMC

Problem Statement

Given the three numbers x,y=xx,z=x(xx)x, y=x^x, z=x^{(x^x)} with .9<x<1.0.9<x<1.0. Arranged in order of increasing magnitude, they are:
<spanclass=′latex−bold′>(A)</span> x,z,y<spanclass=′latex−bold′>(B)</span> x,y,z<spanclass=′latex−bold′>(C)</span> y,x,z<spanclass=′latex−bold′>(D)</span> y,z,x<spanclass=′latex−bold′>(E)</span> z,x,y<span class='latex-bold'>(A)</span>\ x, z, y \qquad<span class='latex-bold'>(B)</span>\ x, y, z \qquad<span class='latex-bold'>(C)</span>\ y, x, z \qquad<span class='latex-bold'>(D)</span>\ y, z, x \qquad<span class='latex-bold'>(E)</span>\ z, x, y
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