Difference between revisions of "2016 AMC 12A Problems/Problem 2"

Latest revision as of 11:46, 4 February 2016

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-==Problem==
+#REDIRECT [[2016 AMC 10A Problems/Problem 2]]
-For what value of <math>x</math> does <math>10^x\cdot100^{2x}=1000^5</math>?
-<math>\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5</math>
-==Solution==
-<cmath>10^x\cdot100^{2x}=10^x\cdot(10^2)^{2x}</cmath>
-<cmath>10^x\cdot10^{4x}=(10^3)^5</cmath>
-<cmath>10^{5x}=10^{15}</cmath>
-<cmath>5x=15</cmath>
-<cmath>x = \boxed{\textbf{(C) } \, 3}</cmath>
-==See Also==
-{{AMC12 box|year=2016|ab=A|num-b=1|num-a=3}}
-{{MAA Notice}}