2003 AMC 10B Problem 9

Attempt Problem 9 of the 2003 AMC 10B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 10B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

Find the value of $x$ that satisfies the equation

$25^{-2} = \dfrac{5^{48/x}}{5^{26/x} \cdot 25^{17/x}}.$

$2$

$3$

$5$

$6$

$9$

Answer: B

Concepts:exponent algebraic manipulation

Difficulty rating: 1070

Solution:

Writing everything base $5,$ the left side is $5^{-4}$ and the right side is $5^{(48-26-34)/x}=5^{-12/x}.$ Setting exponents equal, $-4=-\dfrac{12}{x},$ so $x=3.$

Thus, the correct answer is B.

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