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What is x?

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youenr
 Post subject: What is x?
 Post Posted: Thu Jan 19, 2012 12:49 pm 
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Course Students


Posts: 5
2^x-2^x-2=3(2^13)

solution is 15 but I can't find it!
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ind_sam
 Post subject: Re: What is x?
 Post Posted: Thu Jan 19, 2012 2:11 pm 
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Students


Posts: 1
2^x - 2^x-2 = 3(2^13)
=> 2^(x-2+2) - 2^x-2 = 3(2^13) (x can be written as x-2+2)
=> (2^x-2).(2^2) - 2^x-2 = 3(2^13)
=> 2^x-2(2^2-1) = 3(2^13)
=> 2^x-2(3) = 3(2^13) => x - 2 = 13 => x = 15

Hope it helps :)
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youenr
 Post subject: Re: What is x?
 Post Posted: Thu Jan 19, 2012 2:50 pm 
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Course Students


Posts: 5
thanks for your reply.
Unfortunately I am still confuse :)
how x can be written as x-2+2?
I started with 2^x-2 which for me equal 2x/4, but I am stuck after!
thanks
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jnelson0612
 Post subject: Re: What is x?
 Post Posted: Sun Jan 22, 2012 11:37 pm 
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ManhattanGMAT Staff


Posts: 1857
youenr wrote:
thanks for your reply.
Unfortunately I am still confuse :)
how x can be written as x-2+2?
I started with 2^x-2 which for me equal 2x/4, but I am stuck after!
thanks


Okay, let's try to write this out so it is less confusing:
2^x - 2^(x-2)=3(2^13)

So on the left we have two values, 2^x and 2^(x-2). We want to subtract the second from the first. Whenever we want to add or subtract values with the same bases, express both of them in terms of the SMALLER one. Thus:
2^x = 2^2 * 2^(x-2), which is 4 * 2^(x-2)
AND
2^(x-2) = 1 * 2^(x-2)

So really, it's [4 * 2^(x-2)] - [1 * 2^(x-2)]= 3 * 2^(x-2)

Thus, 3 * 2^(x-2) = 3 * 2^13.
So x-2=13, or x=15.

Hope this helps!

_________________
Jamie Nelson
ManhattanGMAT Instructor
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youenr
 Post subject: Re: What is x?
 Post Posted: Mon Jan 23, 2012 1:41 pm 
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Course Students


Posts: 5
Thanks, got it!
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jnelson0612
 Post subject: Re: What is x?
 Post Posted: Tue Jan 24, 2012 11:10 pm 
Offline
ManhattanGMAT Staff


Posts: 1857
Great, thanks!

_________________
Jamie Nelson
ManhattanGMAT Instructor
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