If 2^x - 2^x-2 = 3(2^13) then the value of x is?

[guest]

If 2^x - 2^x-2 = 3(2^13) then the value of x is?



Some someone please help me with the following:

If 2^x - 2^x-2 = 3(2^13) then the value of x is?

The answer is 15 but I cant figure out how to do it.

Thanks

[blue_lotus]

To solve this question try to make the L.H.S of the equation look similiar to the R.H.S

L.H.S = 2 ^x - 2^(x-2)
= 2^x * (1 - 2^ -2) take 2^x common
= 2^x * (1 - 1/4) since 2^-2 = 1/4
= 2^x * (3/4) note now we have got the 3 we needed
= 2^x * (3/2^2) write 4 as 2^2
= 2^(x-2) * 3

using this in the give equation
2^(x-2) * 3 = 3 ( 2^13)

2^(x-2) = 2^13

x-2 = 13

x = 15

[Guest]

To solve this question try to make the L.H.S of the equation look similiar to the R.H.S

L.H.S = 2 ^x - 2^(x-2)
= 2^x * (1 - 2^ -2) take 2^x common
= 2^x * (1 - 1/4) since 2^-2 = 1/4
= 2^x * (3/4) note now we have got the 3 we needed
= 2^x * (3/2^2) write 4 as 2^2
= 2^(x-2) * 3

using this in the give equation
2^(x-2) * 3 = 3 ( 2^13)

2^(x-2) = 2^13

x-2 = 13

x = 15

This really helps! Thanks alot blue lotus! CHEERS!

[RonPurewal]

someone also posted this question in the gmat verbal (!) section, so we now have two threads on which it is correctly solved.

i guess two threads is better than 0 threads, though.

:)