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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^(2 times x) = 27^(2 times y), which of the following is true?

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Explanation

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

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