Ok you want to get the left side to have the same exponents first.
2^x = (2^2)(2^x-2) : when we multiply items with exponents we are adding the exponents, so 2+x-2 is the same thing as x.
next think of the 2^2 as a 4. (4)(2^x-2)-(2^x-2) is equal to 3(2^x-2)
we now have 3(2^x-2)=3(2^13)
cancel out the threes you get 2^x-2 = 2^13
now just compare the exponents: x-2 = 13
x=15
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value of x
Source: Beat The GMAT — Problem Solving |
2^X- 2^(X-2)= 2^X- 2^X/4
so options 1 ,2 and 3 are out because x must be >13
check for the other two options
2^15- 2^15/4= 2^15-2^13=2^15(4-1)=3*2^13
answer D
so options 1 ,2 and 3 are out because x must be >13
check for the other two options
2^15- 2^15/4= 2^15-2^13=2^15(4-1)=3*2^13
answer D
The powers of two are bloody impolite!!
