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2016 AMC 12A Problem 2

Problem 2 of 25EasierAlgebra

For what value of xx does 10x⋅1002x=10005?10^x\cdot 100^{2x}=1000^5?

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Solution

Since 100=102100=10^2 and 1000=103,1000=10^3, the equation becomes 10x⋅104x=1015, 10^x\cdot 10^{4x}=10^{15}, so 105x=1015.10^{5x}=10^{15}. Then 5x=15,5x=15, giving x=3.x=3. Thus, the correct answer is C.

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Concepts: exponent

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.