Difference between revisions of "2006 AMC 10A Problems/Problem 6"

Revision as of 10:31, 4 July 2013

What non-zero real value for $x$ satisfies $(7x)^{14}=(14x)^7$ ?

$\mathrm{(A) \ } \frac17\qquad \mathrm{(B) \ } \frac27\qquad \mathrm{(C) \ } 1\qquad \mathrm{(D) \ } 7\qquad \mathrm{(E) \ } 14$

Taking the seventh root of both sides, we get $(7x)^2=14x$ .

Simplifying the LHS gives $49x^2=14x$ , which then simplifies to $7x=2$ .

Thus, $x=\frac{2}{7}$ , and the answer is $\mathrm{(B)}$ .

2006 AMC 10A (Problems • Answer Key • Resources)
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All AMC 10 Problems and Solutions

Revision as of 23:11, 27 April 2008 (view source) I like pie (talk \| contribs) (Replaced incorrect solution) ← Older edit		Revision as of 10:31, 4 July 2013 (view source) Nathan wailes (talk \| contribs) Newer edit →
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