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Solve for X as an exponent

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Source: — Problem Solving |
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by gmatmachoman » Sun Sep 26, 2010 9:16 pm
jamesdougnelson wrote:2^x - 2^(x-2) = 3(2^13), solve for x.

This one has really got me stumped. Any help out there?
2^x ( 1 - 1/4) = 3(2^13)

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

2^X = 2 ^15

equating the powers of 2, we have X = 15..
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by Rahul@gurome » Sun Sep 26, 2010 9:19 pm
Solution:
2^x - 2^(x-2) = 2^x - 2^x * 2^(-2)
= 2^x - 2^x/(2^2) = 2^x - 2^x/4 = 2^x(1-1/4)
= 2^x*3/4
So 2^x * ¾ = 3 * 2^13 implies 2^x = 2^13*4 = 2^13*2^2 = 2^15.
Or x = 15.
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