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If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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02 Apr 2012, 14:05
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If \(2^x2^{(x2)}=3*2^{13}\) what is the value of x? A. 9 B. 11 C. 13 D. 15 E. 17
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Last edited by Bunuel on 28 Mar 2016, 02:02, edited 2 times in total.
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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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02 Apr 2012, 18:04
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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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03 Apr 2012, 07:09
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enigma123 wrote: If 2^x2^(x2)=3*2^13 what is the value of x?
A. 9 B. 11 C. 13 D. 15 E. 17 tricky....we would fall for 13...but answer is x2=13 so x=15 i.e D
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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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05 Apr 2013, 00:50
Bunuel wrote: \(2^x(1\frac{1}{2^{2}})=3*2^{13}\) > \(2^x*\frac{3}{2^{2}}=3*2^{13}\). Bunuel, can you tell me what you did in these steps? Where does the 3 come from?



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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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05 Apr 2013, 02:45
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I can explain that: \(2^x2^x^^2=2^x(12^^2)=2^x(1\frac{1}{2^2})=\frac{2^x*3}{4}=3*2^1^3\) divide by 3 \(\frac{2^x}{4}=2^1^3=2^x^^2=2^1^3\) Hope now it's clear
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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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05 Apr 2013, 06:06
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enigma123 wrote: If 2^x2^(x2)=3*2^13 what is the value of x?
A. 9 B. 11 C. 13 D. 15 E. 17 Just another way of doing this sum: \(2^x2^{x2}= (41)*2^{13}\) or \(2^x2^{x2} = 2^{15}2^{13}\) Thus, x = 15.
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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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06 Apr 2013, 06:45
2^x  2^(x2) = {2^(x2)} * ( 2^2  1) = {2^(x2)} * 3 = 3 * 2^13 > 2^(x2) = 2^13 > x2 = 13 > x = 15



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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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23 Jul 2013, 10:18
Zarrolou wrote: I can explain that:
\(2^x2^x^^2=2^x(12^^2)=2^x(1\frac{1}{2^2})=\frac{2^x*3}{4}=3*2^1^3\)
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!
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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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23 Jul 2013, 10:24



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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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23 Jul 2013, 11:51
Bunuel wrote: Step by step:
\(2^x(1\frac{1}{2^{2}})=3*2^{13}\)
\(2^x(\frac{2^21}{2^{2}})=3*2^{13}\)
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..
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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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23 Jul 2013, 12:38



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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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23 Jul 2013, 12:41
Hey, that I understand... but how did u get the 2^2 onto the fraction again to get 2^21/2^2 ? I must miss something very fundamental indeed..
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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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23 Jul 2013, 12:43



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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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23 Jul 2013, 12:49
Bunuel wrote: Can you please tell me what didn't you understand below?
\(2^x2^{x2}=3*2^{13}\)
\(2^x2^{x}*2^{2}=3*2^{13}\)
\(2^x\frac{2^{x}}{2^{2}}=3*2^{13}\)
Hey, sry for not getting it. In the extract shown above I understand everything. What I seem to not get is how you got from 2^x (11/2^2) to 2^x ( 2^21/2^2). Oh wait... did u just multiply with the common denominator (2^2*(1)) ?
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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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23 Jul 2013, 12:57



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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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26 Feb 2014, 20:31
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One more method:
\(2^x  2^{(x2)} = 3 * 2^{13}\)
\(2^x  2^{(x2)} = ( 41 ) * 2^{13}\)
\(2^x  2^{(x2)} = 4 * 2^{13}  1 * 2^{13}\)
\(2^x  2^{(x2)} = 2^{15}  2^{13}\)
Comparing both sides, we get x = 15 = Answer = DWhat 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 (41) & it does the trick
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Last edited by PareshGmat on 27 Oct 2014, 21:30, edited 2 times in total.



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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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18 Aug 2014, 05:54
Has anyone encountered a problem similar to this? Maybe there is a collection of similar problems floating around somewhere? Thanks!



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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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18 Aug 2014, 06:58
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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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30 Aug 2014, 06:14
Hello everyone,
this question came up as one of the early ones in my gmat prep exam (scored very badly). Is this really a sub600 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.



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Re: If 2^x2^(x2)=3*2^13 what is the value of x? [#permalink]
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28 Oct 2014, 10:54
Do you keep your work? If so, at which step did you mess up? Also, make sure you can verbally explain why you did each step.




Re: If 2^x2^(x2)=3*2^13 what is the value of x?
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