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Hey ! Unfortunately, I still don't get where that '3' comes from... Just don't see it... Could anyone explain further in more detail?! Would be great!
_________________

Concentration: Entrepreneurship, General Management

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

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23 Jul 2013, 10:51

Bunuel wrote:

Step by step:

\(2^x(1-\frac{1}{2^{2}})=3*2^{13}\)

\(2^x(\frac{2^2-1}{2^{2}})=3*2^{13}\)

Hey, now its clear where the 3 comes from but how did u get the 2^2 there? Sry, was a long day... I bet its easy as hell but I'm just confused atm..
_________________

Concentration: Entrepreneurship, General Management

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

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23 Jul 2013, 11:41

Hey, that I understand... but how did u get the 2^2 onto the fraction again to get 2^2-1/2^2 ? I must miss something very fundamental indeed..
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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26 Feb 2014, 19:31

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One more method:

\(2^x - 2^{(x-2)} = 3 * 2^{13}\)

\(2^x - 2^{(x-2)} = ( 4-1 ) * 2^{13}\)

\(2^x - 2^{(x-2)} = 4 * 2^{13} - 1 * 2^{13}\)

\(2^x - 2^{(x-2)} = 2^{15} - 2^{13}\)

Comparing both sides, we get x = 15 = Answer = D

What I like about this method is we need not have to expand/solve the LHS of the equation. Just adjust 3 of the RHS as (4-1) & it does the trick
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Last edited by PareshGmat on 27 Oct 2014, 20:30, edited 2 times in total.

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

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30 Aug 2014, 05:14

Hello everyone,

this question came up as one of the early ones in my gmat prep exam (scored very badly). Is this really a sub-600 question?

I always have struggles with those questions (exponents, roots), but I DO REALLY understand the explanation. However, as soon as I come across a similar problem, I never know how to approach it correctly.. Does anyone have some tips? I already practiced a lot of similar problems, but it's seems that I am still not improving.