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

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Intern
Joined: 24 May 2014
Posts: 13
Location: Brazil
If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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25 Jun 2014, 18:24
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Difficulty:

55% (hard)

Question Stats:

69% (01:59) correct 31% (02:31) wrong based on 458 sessions

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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
Director
Joined: 25 Apr 2012
Posts: 721
Location: India
GPA: 3.21
Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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25 Jun 2014, 20:00
2
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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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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)

$$= \frac{1}{15}$$

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Joined: 07 Apr 2015
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Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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05 Sep 2015, 04:00
1
KUDOS
can somebody pls format the question properly? Question stem let me think that it was $$(2^1-x)^2$$ and not $$(2^{1-x})^2$$
Math Expert
Joined: 02 Sep 2009
Posts: 43363
Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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

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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.
Intern
Joined: 26 Apr 2016
Posts: 8
Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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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).
Math Expert
Joined: 02 Sep 2009
Posts: 43363
Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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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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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

Why is this not the correct way to approach?

Math Expert
Joined: 02 Sep 2009
Posts: 43363
Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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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

Why is this not the correct way to approach?

$$2^{4x} = 2^4*3^2*5^2$$. 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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19 Nov 2017, 10:21
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Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ? [#permalink]

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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

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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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