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exponent problem

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Junior | Next Rank: 30 Posts
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by walkingbanana » Sun Feb 08, 2009 8:50 pm
Hi everyone,

This forum has been a fantastic source of information for me and I just want to thank everyone for their helpful posts.

I'm reviewing my first GMAT PREP CAT but i'm stumped on how to solve this question.

if 2^x - 2^(x-2) = 3* (2^13), what is x?

can anyone offer some enlightenment?

answer: 15
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Master | Next Rank: 500 Posts
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by gaggleofgirls » Sun Feb 08, 2009 9:27 pm
2^x - 2^(x-2) can only be dealt with by factoring....

= 2^(x-2) * (2^2 - 1) becuase 2^2 * 2(x-2) = 2^2+x-2 = 2^x

= 2^(x-2) (4-1)

= 2^(x-2) * 3

SO

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

2^(x-2) = 2^13
x-2 = 13
x = 15

-Carrie
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Junior | Next Rank: 30 Posts
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by walkingbanana » Sun Feb 08, 2009 9:49 pm
ohhhhhh i c now. nice hack. thanks!!
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