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Exponent Problem

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by alicia » Sat Sep 17, 2011 9:21 am
This was a problem on my practice test. Please advise on the step by step solution/breakdown for this problem:

If 2^x - 2^x-2 = 3(2^13), what is the value of x?

a. 9
b. 11
c. 13
d. 15
e. 17

The correct answer is d. 15
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by cans » Sat Sep 17, 2011 9:28 am
2^x - 2^x-2 = 3(2^13)
i think the problem is like this : 2^x - 2^(x-2) = 3(2^13)
-> 2^x - 2^x/4 = 3(2^13) (as 2^(a-b) can be written as 2^a / 2^b)
4* 2^x - 2^x = 3(2^13)*4
3*2^x = 3(2^13)*(2^2)
2^x = 2^(13+2) = 2^15
thus x=15
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by alicia » Sat Sep 17, 2011 8:03 pm
Thanks!

However, I don't understand how you got from 2^x-2 to 2^x/4

Please explain.
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by cans » Sat Sep 17, 2011 9:49 pm
2^(x-2) to (2^x)/4
lhs: (2^x)*(2^(-2)) = (2^x)/4
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by GMATGuruNY » Sun Sep 18, 2011 3:42 am
Can's solution is great. For a less algebraic approach, check here:

https://www.beatthegmat.com/2-x-2-x-2-3- ... tml#309765
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by Abhishek009 » Sun Sep 18, 2011 4:30 am
alicia wrote:This was a problem on my practice test. Please advise on the step by step solution/breakdown for this problem:

If 2^x - 2^x-2 = 3(2^13), what is the value of x?

a. 9
b. 11
c. 13
d. 15
e. 17

The correct answer is d. 15
2^x - 2^x-2 = 3(2^13)

Or, 2^x - 2^x-2 = {(2^2) - 1}(2^13)

Or , 2^x - 2^x-2 = 2^15 -2^13


Now we can safely claim x = 15...
Abhishek
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by leumas » Thu Sep 22, 2011 9:31 am
alicia wrote:This was a problem on my practice test. Please advise on the step by step solution/breakdown for this problem:

If 2^x - 2^x-2 = 3(2^13), what is the value of x?

a. 9
b. 11
c. 13
d. 15
e. 17

The correct answer is d. 15
There can be only two options. 15 or 17 since rhs has 2^13

Now: (2^x - 2^(x-2))/ 2^13 = 3

Substitute 15: Answer will be 4-1 =3 Success!
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