2006 AMC 10A Problem 6

Problem 6 of 25EasierAlgebra

What non-zero real value for

x

satisfies

(7x)^{14} = (14x)^7?

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Solution

Taking the seventh root of both sides gives

(7x)^2 = 14x,

49x^2 = 14x.

Since

x \neq 0,

divide by

x

to get

49x = 14,

hence

x = \dfrac{2}{7}.

Thus, the correct answer is B.

Concepts: exponent · algebraic manipulation

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