Need help with exponents

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dkim0105: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Wed Aug 18, 2010 12:19 pm

by dkim0105 » Wed Aug 18, 2010 1:27 pm

Im working on the GMAT and can't figure this out. Forgot how to remove exponents.

3^x - 3^x-1 = 162... what is x(x-1)?

and

2^x - x^x-2 = 3(2^13)... what is x?

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Source: Beat The GMAT — Quantitative Reasoning | Wed Aug 18, 2010 1:27 pm

Tani: Legendary Member; Posts: 1255; Joined: Fri Nov 07, 2008 2:08 pmFollowed by: 90 members; Location: St. Louis; Thanked: 312 times

by Tani » Wed Aug 18, 2010 1:35 pm

factoring out 3^(x-1) you get
3^(x-1) * (3^1 - 1) or 3^(x-1) *2 = 162
therefor 3^(x-1) = 81
but 3^4 = 81 so x = 5.
x*(x-1) = 5*4 = 20

I suspect you copied the second one incorrectly and are asking about
2^x - 2^(x-2) = 3(2^13)

IN that case you get 2^(x-2) * (2^2 - 1) = 2^(x-2) * (4-1) = 3 * 2^(x-2)
therefore x-2 = 13 and x = 15

Tani Wolff

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dkim0105: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Wed Aug 18, 2010 12:19 pm

by dkim0105 » Wed Aug 18, 2010 1:53 pm

wow, awesome, thanks for the quick reply. I just stumbled onto this forum and it is amazing.

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Tani: Legendary Member; Posts: 1255; Joined: Fri Nov 07, 2008 2:08 pmFollowed by: 90 members; Location: St. Louis; Thanked: 312 times

by Tani » Wed Aug 18, 2010 5:05 pm

Glad to help!

Tani Wolff

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