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Just as you'd factor out the term with the smaller power if you saw something like \(x^8 - x^7\) (you'd factor out \(x^7\)) you can factor out the term with the smaller power here:

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It seems like you were really close but you solved for x - 1 instead. I am curious - how did you reason through the question? Perhaps you figured the answer has to be in the form of x(x -1), e.g. (3)(4) = 12. Even then, had you figured x has to be a little bigger (plugging in 4 for x gives you 81 which is too low), So when you reasoned the answer to be 4 you may have plugged the 4 in the (x - 1) exponent place.

Again, a quick plugging in should get you (C) 20 as (E), the only other answer with consecutive integers as factors is far too big.
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Re: If 3^x - 3^(x-1) = 162, then x(x - 1) = [#permalink]

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Re: If 3^x - 3^(x-1) = 162 then x(x-1) = [#permalink]

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22 Feb 2017, 12:28

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Re: If 3^x - 3^(x-1) = 162, then x(x - 1) = [#permalink]

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22 Feb 2017, 15:09

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Given: 3^x - 3^(x-1) = 162 Factor to get: [3^(x-1)][3^1 - 1] = 162 Simplify to get: [3^(x-1)][2] = 162 Divide both sides by 2 to get: 3^(x-1) = 81 Rewrite the right side as 3^(x-1) = 3^4 So, x - 1 = 4 This means x = 5