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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 ? [#permalink]

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New post 25 Jun 2014, 18:24
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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
[Reveal] Spoiler: OA
2 KUDOS received
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Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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New post 25 Jun 2014, 20:00
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Reni wrote:
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

[Reveal] Spoiler:
B


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
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Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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New post 10 Jul 2014, 02:35
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\(2^{4x} = 3600\)

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

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

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

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

\(= \frac{1}{15}\)

Answer = B
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Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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New post 05 Sep 2015, 04:00
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can somebody pls format the question properly? Question stem let me think that it was \((2^1-x)^2\) and not \((2^{1-x})^2\)
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Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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New post 06 Sep 2015, 03:42
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Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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New post 20 Nov 2015, 01:38
Bunuel wrote:
noTh1ng wrote:
can somebody pls format the question properly? Question stem let me think that it was \((2^1-x)^2\) and not \((2^{1-x})^2\)

_______________
Edited. Thank you.


Wait, \((2^{1-x})^{2}\) is the same with \(2^{(1-x)^{2}}\) ?

I thought the first were equal to \(\left(\frac{2}{2^x}\right)^{2}\), and the second equal to \(\left(\frac{2}{2^x}\right) * 2^{(x^{2})}\)?

And could you pls tell me how to calculate \(2^{(x^{2})}\) if I (unfortunately) encounter it in the test? Thanks Bunuel.
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Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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New post 08 Jul 2016, 10:57
Reni wrote:
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


Is it \(2^{(1-x)^2}\) as written in the original post? Or (2^(1-x))^2 as in the answer solutions? The question stem multiplies to be 2^(x^2 - 2x + 1).
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Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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New post 08 Jul 2016, 11:43
DavidFox wrote:
Reni wrote:
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


Is it \(2^{(1-x)^2}\) as written in the original post? Or (2^(1-x))^2 as in the answer solutions? The question stem multiplies to be 2^(x^2 - 2x + 1).

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It's \((2^{(1-x)})^2\)
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Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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New post 04 Nov 2016, 19:46
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 :)
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Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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New post 05 Nov 2016, 01:08
lawiniecke wrote:
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 :)


\(2^{4x} = 2^4*3^2*5^2\). If x=1, then you'd get that \(1 = 3^2*5^2\), which is wrong --> \(x \neq 1\). In fact from \(2^{4x} = 3600\) it follows that x is some irrational number (approximately 2.9534...), not an integer.
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Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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New post 22 Nov 2017, 11:27
Reni wrote:
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


Let’s first simplify the expression we want to evaluate. We see that [2^(1-x)]^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
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Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ?   [#permalink] 22 Nov 2017, 11:27
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