2016 AMC 10A Problems/Problem 2: Difference between revisions
Math101010 (talk | contribs) Created page with "For what value of <math>x</math> does <math>10^{x}\cdot 100^{2x}=1000^{5}</math>? <math>\textbf{(A)}\ 1 \qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\..." |
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<math>\textbf{(A)}\ 1 \qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5</math> | <math>\textbf{(A)}\ 1 \qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5</math> | ||
==Solution== | |||
We can rewrite <math>10^{x}\cdot 100^{2x}=1000^{5}</math> as <math>10^{5x}=10^{15}</math>. From here, we can easily solve for <math>x</math>, and <cmath>x = \boxed{\textbf{(C)}\;3.}</cmath> | |||
Revision as of 18:10, 3 February 2016
For what value of 
does 
?
Solution
We can rewrite as 
. From here, we can easily solve for , and ![\[x = \boxed{\textbf{(C)}\;3.}\]](http://latex.artofproblemsolving.com/c/9/e/c9ea0e5d997f4eec8aa2c848000e61ed00284ef9.png)
