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Exponents, find value of X

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by Frankenstein » Mon Jul 04, 2011 7:08 pm
Hi,
2^x = 2^(x-2+2) = 2^2*2^(x-2) = 4.2^(x-2)
So, 2^x - 2^x-2 = 4*2^(x-2) - 2^(x-2) = 3*2^(x-2) = 3*2^13
So, x-2 = 13 => x=15

Hence, D
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by sunilrawat » Mon Jul 04, 2011 8:58 pm
rerika01 wrote: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 answer is 15. I just don't know how to get to 15.

thanks!
2^x - 2^x-2 = 3(2^13)
2^x(1 - 2^-2) = 3(2^13)
3*2^(x-2) = 3(2^13)
x-2 = 13,
x = 15
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