Always think about checking your work by substituting the answer you got back into the question
In any case
taking 2^(X-2) common you get
2^(X-2)[2^2 -1] = 3(2^13)
2^(X-2)[3] = 3(2^13)
Thus you can see that 2^(X-2)=(2^13)
OR X-2 = 13
X = 15
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prep question
Source: Beat The GMAT — Problem Solving |
2^x - 2^(x-2) = 3 (2^13)
Take 2^(x-2) common here
2^(x-2)*[2^2 - 1] = 3(2^13)
2^(x-2)*[4-1]= 3(2^13)
2^(x-2)*[3]= 3(2^13)
2^(x-2)=2^13
Or x-2=13
Thus x = 15(base of the two powers are the same so equate the powers)
Take 2^(x-2) common here
2^(x-2)*[2^2 - 1] = 3(2^13)
2^(x-2)*[4-1]= 3(2^13)
2^(x-2)*[3]= 3(2^13)
2^(x-2)=2^13
Or x-2=13
Thus x = 15(base of the two powers are the same so equate the powers)
