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2007 AMC 10AProblem 9P1-10~2 minPrint
Exponents, Logarithms & RadicalsSystems of EquationsSet up the equation/formula and compute; no special trick needed

Real numbers aa and bb satisfy the equations 3a=81b+23^{a} = 81^{b + 2} and 125b=5a−3125^{b} = 5^{a - 3} . What is abab ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.