If 2^4x = 3,600, what is the value of (2^1-x)^2 ?

Question

If  2^{4x} = 3,600 , what is the value of  (2^{(1-x)})^2  ?

(A) -1/15
(B) 1/15
(C) 3/10
(D) -3/10
(E) 1

PareshGmat · Accepted Answer

2^{4x} = 3600

(2^{2x})^2 = 60^2

2^{2x} = 60  .............. (1)

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

= \frac{4}{60} .............. (From 1)

= \frac{1}{15}

Answer = B

JeffTargetTestPrep · Answer

Let’s first simplify the expression we want to evaluate. We see that  ^2 can be simplified as (2 * 2^-x)^2 = 2^2 * 2^-2x = (2^2)/(2^2x)

Thus, if we can determine 2^2x, then we have an answer.

Taking the square root of both sides of the given equation, which is 2^4x = 3600 we have 2^2x = 60; thus:

(2^2)/(2^2x) = 4/60 = 1/15

Answer: B

WoundedTiger · Answer

Given 2^4x=1600 We need to find value of 2 ^(1-x)^2-------> Simplify this term (\frac{2}{2^x})^2 So we need to find value of \frac{4}{2^{2x}} 2^4x=3600. Taking a square root we get 2^2x=60 So we get 4/60 or 1/15 Ans is B Similar question or practice: given-2-4x-1600-what-is-the-value-of-154486.html#p1236720 if-4-4x-1600-what-is-the-value-of-4-x-161823.html

law258 · Answer

Can someone please explain why we can't do the following: Break 3600 to 2^4 x (3^2) x (5^2) --> so x=1 making the answer 1. Why is this not the correct way to approach? Thanks in advance

Bunuel · Answer

2^{4x} = 2^4*3^2*5^2 . If x=1, then you'd get that  1 = 3^2*5^2 , which is wrong -->  x 
eq 1 . In fact from  2^{4x} = 3600  it follows that x is some irrational number (approximately 2.9534...), not an integer.

SVaidyaraman · Answer

2^(4x)= 3600 => x is just less than 3
=>2^((1-x))^2 = approx (2^(1-3))^2= approx 1/(2^4) 
Hence B.

BrentGMATPrepNow · Answer

GIVEN: 2^(4x) = 3,600
Raise both sides to the power of 1/2 to get:  ^(1/2) = 3,600^(1/2)
Simplify:  2^(2x) = 60

We want to find the value of:  ²
To simplify, apply Power of Power law to get: 2^(2 - 2x)
This is equal to: (2^2)/ 
Replace  2^(2x)  with  60  to get: (2^2)/ 60  = 4/60 = 1/15

Answer: B

RELATED VIDEO FROM OUR COURSE
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prathyushaR · Answer

(2^1-x)^2 = 2^2/2^2x
so, (a^m)^n = a^(m*n) Right?
so (2^1-x)^2=2^((1-x)*2)=2^(2-2x)
now, a^(m-n)=(a^m)/(a^n) okay?
thus,
2^(2-2x) = 2^2/2^2x

levin343 · Answer

Sorry I want to ask my approach in this qn and why this may be or may not be right

So I first simplify the equation that we want to find out

2^2(1-x) 
2^2/ 2^(2x) eq 1

then I want to find out how to solve this problem, but my approach is slightly not conventional (just my brain not thinking of square-root but okay, i want to ask participants here on this

so I saw 2^4x = 3600

meaning 2^4x = 2^4 x 3^2 x 5^2 
in a way 2^4x = 2^2 (2^2 x 3^2 x 5^2)
then 2^4x = 2^2 (30^2) 
then 2^4x/ 30^2 = 2^2 eq 2

So I put back the 2^2 to the eq 1

(2^4x/30^2) / 2^2x

2^2x / 30 x 1/2^2x = the 2^2x crossed out

so I got 1/30 instead---> can see where it goes wrong?

kop18 · Answer

Hi  levin343 ,

I'm not sure if this is still helpful but please see the worked out problem in the file attached. I'm finding it hard to follow what is going on in this step.
(2^4x/30^2) / 2^2x
2^2x / 30 x 1/2^2x = the 2^2x crossed out

If u follow then snip attached below it may be helpful to understand that we never really get rid of 2^2x. Hence, we cannot get 1/30.

Posted from my mobile device

krishna_sunder_ · Answer

2^(2*(1-x)) 
= 2^(2-2x) 
= (2^2)/(2^(2x)) 
= 4/2^(2x) 
= root  
= root(16/3600) 
= 4/60 
= 1/15

GMATinsight · Answer

(2^{(1-x)})^2 = 2^{2-2x} = 2^2/2^{2x}

SInce  2^{4x} = 3,600 
so  2^{2x} = 60  (taking square root both sides)

Hence,  2^2/2^{2x} = 4/60 = 1/15

Answer: Option B

minionbaba · Answer

Hi Bunuel , can you help in having this note below the question for everyone's benefit? Thanks! Similar question: https://gmatclub.com/forum/if-3-6x-8-10 ... l#p3787306

If 2^4x = 3,600, what is the value of (2^1-x)^2 ?

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If 2^4x = 3,600, what is the value of (2^1-x)^2 ?

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