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

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If 2^x - 2^(x-2) = 3*2^13, what is the value of x? [#permalink]

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03 Dec 2010, 09:37
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If 2^x - 2^(x-2) = 3*2^13, what is the value of x?
A. 9
B. 11
C. 13
D. 15
E. 17
[Reveal] Spoiler: OA
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03 Dec 2010, 10:38
emk60 wrote:
I am having trouble understanding this... I can't remember whose notes this is from, but it is something I printed off this site.

7^4 + 7^7
= 7^4(1+7^3)
=7^4(50)

And

3^4+12^4
=3^4+ (3*4)^4
=3^4(1+4^4)
=3^4(256)

In both instances I am confused with what happens to the one in the second to last step. Wouldn't it be 3^4+3^4(256)? It seems like the 1 just disappears???

Here is a problem I can not solve:

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

x=?

The answer is 15 but I do not understand how to get it. Is there a good guide online or does someone have good notes for exponents? I am lacking in this area and I need it dumbed down.

Provide answer choices for PS questions.
Make sure you type the question in exactly as it was stated from the source.

1. $$7^4+7^7$$ --> factor out 7^4 --> $$7^4(1+7^3)=7^4(1+343)=7^4*344$$ (so the answer given in your example is not correct);

2. $$3^4+12^4=3^4+(3*4)^4=3^4+3^4*4^4$$ --> factor out 3^4 --> $$3^4(1+4^4)=3^4(1+256)=3^4*257$$ (so again the answer given in your example is not correct).

The question itself:
If 2^x - 2^(x-2) = 3*2^13, what is the value of x?
A. 9
B. 11
C. 13
D. 15
E. 17

$$2^x - 2^{x-2} = 3*2^{13}$$ --> factor out $$2^{x-2}$$ --> $$2^{x-2}*(2^2-1)=3*2^{13}$$ --> $$2^{x-2}*3=3*2^{13}$$ --> $$2^{x-2}=2^{13}$$ --> $$x-2=13$$ --> $$x=15$$.

Other solutions at: solving-exponents-ii-104831.html

For more on number theory an exponents check: math-number-theory-88376.html

DS questions on exponents: search.php?search_id=tag&tag_id=39
PS questions on exponents: search.php?search_id=tag&tag_id=60

Hope it helps.
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03 Dec 2010, 11:18
I do not have a link for the examples I provided but they are from Slingfox's Condensed GMAT Strategies.

Thanks for the explaination. It was the incorrect examples that threw me off.
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