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by das.ashmita » Sun Oct 07, 2012 12:14 pm
Hi Pritam


4^4x = 1600
4^2x = root(1600) = 40.... (1)

We need to find 4^(x-1)2 = (4^2x)/ (4^2)
Substituting (1), we get
= 40/16 = 2.5

ANS 2.5
Last edited by das.ashmita on Sun Oct 07, 2012 9:55 pm, edited 4 times in total.
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by das.ashmita » Sun Oct 07, 2012 12:15 pm
4^2x=|root(1600)| and how you get 400? 400^2=160000
and 4^(x-1)2 is meant to be 4^(x-1)^2 - We don't factor by 2 at the end of exponential expression
I have edited my post above. Root(1600) = 400 was a blunder on my part. :( . It should be 40.

Regarding expression "4^(x-1)2 ", it cannot possibly be "4^(x-1)^2" in this question as it would yield no result. :P

The proper interpretation is given below:
4^(x-1)2 = [4^(x-1)]^2 or 4^2(x-1)
Last edited by das.ashmita on Sun Oct 07, 2012 9:55 pm, edited 3 times in total.
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by pemdas » Sun Oct 07, 2012 1:11 pm
4^2x=|root(1600)| and how you get 400? 400^2=160000
and 4^(x-1)2 is meant to be 4^(x-1)^2 - We don't factor by 2 at the end of exponential expression :)
das.ashmita wrote:Hi Pritam


4^4x = 1600
4^2x = root(1600) = 400.... (1)

We need to find 4^(x-1)2 = (4^2x)/ (4^2)
Substituting (1), we get
= 400/16 = 25

ANS 25
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by pemdas » Sun Oct 07, 2012 1:39 pm
pritam.ryders wrote:If 4^4x = 1600 then what is the value of 4^(x-1)2 ?
the required is 4^(x-1)^2 along with 4^(x^2-2x+1) or (4^(x-1))^2 ??
I hope the latter is our needed condition, as with 4^(x-1)^2 we fall to the given 4^4x=1600, 4^2x=|40| and 4^2x=|4*10| and consider positive case first, 4^(2x-1)=10. From the above expression we have an exponent (x^2-2x+1) and we can rewrite 4^(2x-1)=10 as 4^(-2x+1)=1/10. So we have 1/10 * 4^(x^2) where 4^(x^2) is unknown.

If are given (4^(x-1))^2, then 4^(2x-2) is sought for solution. Since 4^(2x-1)=10, 4^(2x-2)=10/4=2.5
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by GMATGuruNY » Sun Oct 07, 2012 2:57 pm
pritam.ryders wrote:If 4^4x = 1600, then what is the value of (4^(x-1))² ?

40
20
10
5/2
5/4
Rephrase (4^(x-1))² into a form resembling 4^4x:
(4^(x-1))²

= 4^(2x-2)

= (4^2x)/4²

= (4^2x)/16.

Use 4^4x = 1600 to determine the value of 4^2x:
4^2x = (4^4x)^(½) = 1600^(½) = 40.

Substitute 4^2x = 40 into (4^2x)/16:
(4^2x)/16 = 40/16 = 5/2.

The correct answer is D.
Last edited by GMATGuruNY on Mon Oct 08, 2012 2:51 am, edited 1 time in total.
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by pemdas » Mon Oct 08, 2012 12:33 am
But Mitch with your notation, 4^(x-1)^2 falls into 4^(x^2-2x+1)

should not this be (4^(x-1))^2 by squaring the entire expression?
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by GMATGuruNY » Mon Oct 08, 2012 2:57 am
pemdas wrote: Should not this be (4^(x-1))^2 by squaring the entire expression?
Yes, indeed. The problem asks for the value of (4^(x-1))². I've corrected the notation in my post above.
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