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# ps - exponents

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VP
Joined: 30 Sep 2004
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Location: Germany
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ps - exponents [#permalink]  07 Aug 2005, 12:00
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if 2^x - 2^(x-2) = 3(2^13). what is x ?
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Intern
Joined: 19 Aug 2004
Posts: 47
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Kudos [?]: 3 [0], given: 0

First, 2^(x-2) = (2^x)/4

So, 2^x - 2^(x-2) = [3 * 2^x]/4

(3*2^x)/4 = 3 * (2^13)

3 * 2^x = 3 * 2^15

So, x = 15.
Manager
Joined: 06 Aug 2005
Posts: 197
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Yes exactly, it is probably a bit neater to keep (x-2) on the left.

2^x - 2^(x-2) = 4 (2 ^ (x-2)) - (2 ^ (x-2))
= 3 x 2^(x-2) = 3 x 2 ^ (13)

So x-2 = 13 and hence x=15
SVP
Joined: 14 Dec 2004
Posts: 1707
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Kudos [?]: 50 [0], given: 0

2^x * (1 - (1/4)) = 3(2^13)

2^x * (3/4) = 3(2^13)

2^(x-2) = 2^13

x-2=13

x=15.
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