Exponent problem

[saracuse]

Need some quick help on this seemingly easy problem:

2^x - 2^(x-2) = 3(2^13) what is x?
the answer is 15.


3? i know im supposed to simplify so that i can just add/subtract exponents. but the [x-(x-2)] seem to be canceling each other out?

any thoughts?

thanks all!

[xcusemeplz2009]

simplify is just what we need to do here

2^x-2^(x-2)=2^x-2^x/2^2=2^x(1-1/4)=2^x*(3/4)=2^(x-2)*3
now equate 2^(x-2)*3=(2^13)*3=> x-2=13;x=15

[viju9162]

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

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

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

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

x-2=13; x=15

Hi saracuse,
x-(x-2)doesnt cancel off ... it will be like this : 2^x/2^2 ... then u can follow the above steps...

Hope this helps..

[saracuse]

This is very helpful thank you!