GMAT QUESTION(Can someone explain)

[gettin there]

If 2^x - 2^x-2 = 3(2^13), what is the value of x?
*9 *11 *13 *15 *17

[hwiya320]

is the OA = 15?

I'm assuming the question is

2^x - 2^(x-2) = 3(2^13) ?

then take out 2^x

2^x * (1 - 2^-2) = 3(2^13)
equals => 2^x * (3/4) = 3(2^13)

then that also equals 2^x * (3/ 2^2) = 3(2^13)

2^x / 2^2 = 2^13
15-2 = 13

so x = 15?

[canuckclint]

I worked it out and 15 is right.

Btw, you will want to put brackets on your exponent (x-2) for next time.

[dmateer25]

I took 2 approaches with this.

1 similar to hwiya320.

The second I plugged in the numbers. This exponent problem was actually friendly for plugging in.

Starting with choice E

2^17 - 2^(17-2) = 3(2^13)
2^17 - 2^15 =
2^15(2^2-1) =
2^15(3)

No this isn't right

Next D

2^15 - 2^(15-2) = 3(2^13)
2^15 - 2^13 =
2^13 (2^2 - 1) =
2^13(3)

Bingo, 15 it is

[720dreaming]

you could also divide the first expression by 2^13. This gives you:

2^(x-13) - 2^(x-15)=3

Should be easier to plug in answers this way w/o doing additional work.