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20

Part of 1991 AMC 12/AHSME

Problems(1)

Exponents

Source: AHSME 1991 problem 20

10/30/2011
The sum of all real xx such that (2x−4)3+(4x−2)3=(4x+2x−6)3(2^{x} - 4)^{3} + (4^{x} - 2)^{3} = (4^{x} + 2^{x} - 6)^{3} is
<spanclass=′latex−bold′>(A)</span> 3/2<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 5/2<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> 7/2 <span class='latex-bold'>(A)</span>\ 3/2\qquad<span class='latex-bold'>(B)</span>\ 2\qquad<span class='latex-bold'>(C)</span>\ 5/2\qquad<span class='latex-bold'>(D)</span>\ 3\qquad<span class='latex-bold'>(E)</span>\ 7/2
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