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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

If x is greater than 0 and y is greater than 0, and if 3^(2x) = 27^(2y), which of the following is true?

(A) x = y
(B) x = 2y
(C) 2x = y
(D) x = 3y
(E) 3x = y

答案和解析

答案：D

解析：

If x is greater than 0 and y is greater than 0, and if 3^(2x) = 27^(2y), then rewriting 27 as 3^3 gives 3^(2x) = 27^(2y) = (3^3)^(2y) = 3^(3(2y)). It follows that 3^(2x) = 3^(3(2y)) = 3^(6y), and so 2x = 6y. This last equation is equivalent to x = 3y.