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

(No difference)

Revision as of 01:55, 6 July 2006


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

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


We first break up 14 into (7x)(2), so that

$(7x)^{14}=(7x\cdot 2)^7\Longrightarrow (7x)^{14}=((7x)^7)(2^7)$

We then divide out $(7x)^7$



We take the 7th root of each side.


$7x=2\Longrightarrow x=\frac{2}{7}, (B)$

See Also

Invalid username
Login to AoPS