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Nested Logarithms

Source: 1971 AHSME Problem 21

April 22, 2014
logarithmsAMC

Problem Statement

If log⁡2(log⁡3(log⁡4x))=log⁡3(log⁡4(log⁡2y))=log⁡4(log⁡2(log⁡3z))=0\log_2(\log_3(\log_4 x))=\log_3(\log_4(\log_2 y))=\log_4(\log_2(\log_3 z))=0, then the sum x+y+zx+y+z is equal to
<spanclass=′latex−bold′>(A)</span>50<spanclass=′latex−bold′>(B)</span>58<spanclass=′latex−bold′>(C)</span>89<spanclass=′latex−bold′>(D)</span>111<spanclass=′latex−bold′>(E)</span>1296<span class='latex-bold'>(A) </span>50\qquad<span class='latex-bold'>(B) </span>58\qquad<span class='latex-bold'>(C) </span>89\qquad<span class='latex-bold'>(D) </span>111\qquad <span class='latex-bold'>(E) </span>1296
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