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exponent problem again......

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by Mr.Hollywood » Wed Mar 14, 2012 9:59 pm
6^x=8100, what is(1/3)^(x-3)

I dont have the answer choices, I'd probably plug it in.
However I was wondering if anybody know how to solve this without answer choices provided?

Thanks!
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Source: — Problem Solving |

by GMATGuruNY » Thu Mar 15, 2012 3:24 am
Image

The correct problem appears above.

3^6x = 8100
(3^3x)² = 8100
3^3x = 90.

(3^(x-1))^3
= 3^(3x-3)
= (3^3x)/3³
= 90/27 (substituting 3^3x = 90)
= 10/3.

The correct answer is D.
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