Another exponent problem

[eclaym2003]

If (2^x)-(2^(x-1))=3(2^13), what is the value of x?

[tdadic84]

i think the question is wrong...

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

and the answer should be x = 15....

[eclaym2003]

thanks ... your right it is wrong ... it was right the way that you worked it.

[eclaym2003]

How did you get that answer?

[tdadic84]

I know there is a more "formal" way...but i just dumbed it down and it usually works for me

so..for the right side i used 2^3 instead of 2^13 (to make it easier) ...so the right side is (3)2^3 = 24...

now...you know the squares of the first 5 2's is.. 2, 3 , 8, 16, 32....and 32-8=24...

sooo 2^5-2^3 = 3(2^13)....therefore if you see the pattern...
2^x -2^x-2 = 2^15-2^13 = 3(2^13)..hence x=15...

[rah_pandey]

the correct problem if solved is 2^x(3/4)=3*2^13,
2^(x-2)*3=3*2^13 now match the powers of 2on both sides=> x-2=13,=>x=15

[exhilaration]

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

1) Factor out the 2^x-2

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

2) Simplify

2^2 = 4

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

3) Divide both sides by 3
2^x-2 = 2 ^13

4) solve for x
x-2 = 13

X= 15

[eclaym2003]

Thanks you guys ... I gainged insight by exhilarations breakdown. I am having one little issue, though. I am lost whenever you factor out 2^x-2. I am a little lost whenever you factor it out of 2^x and how 2^2 results. Everthing else is great... that is my one little gap.

[exhilaration]

Thanks you guys ... I gainged insight by exhilarations breakdown. I am having one little issue, though. I am lost whenever you factor out 2^x-2. I am a little lost whenever you factor it out of 2^x and how 2^2 results. Everthing else is great... that is my one little gap.

When you factor out 2^X-2 from 2^X, you are subtracting the exponents. So you get X-(X-2) = X-X+2 = 2, resulting in 2^2.

For example, 5^5 - 5^4.

If you factor out 5^4 = 5^4(5-1)

If you factor out 5^5 = 5^5 (1-1/5)

[eclaym2003]

OMG, that definitely cleared things thanks again!!!