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Exponents a,b,c,d

Source: AHSME 1963 Problem 13

January 9, 2014
AMC

Problem Statement

If 2a+2b=3c+3d2^a+2^b=3^c+3^d, the number of integers a,b,c,da,b,c,d which can possibly be negative, is, at most:
<spanclass=′latex−bold′>(A)</span> 4<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> 1<spanclass=′latex−bold′>(E)</span> 0<span class='latex-bold'>(A)</span>\ 4 \qquad <span class='latex-bold'>(B)</span>\ 3 \qquad <span class='latex-bold'>(C)</span>\ 2 \qquad <span class='latex-bold'>(D)</span>\ 1 \qquad <span class='latex-bold'>(E)</span>\ 0
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