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

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Question Stats: 69% (02:27) correct 31% (02:28) wrong based on 743 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
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1732
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ?  [#permalink]

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43
14
$$2^{4x} = 3600$$

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

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

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

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

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

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

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4
3
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

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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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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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 V
Joined: 02 Sep 2009
Posts: 58964
Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ?  [#permalink]

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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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1
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?

Thanks in advance Math Expert V
Joined: 02 Sep 2009
Posts: 58964
Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ?  [#permalink]

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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?

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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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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Director  S
Joined: 17 Dec 2012
Posts: 623
Location: India
Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ?  [#permalink]

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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

2^(4x)= 3600 => x is just less than 3
=>2^((1-x))^2 = approx (2^(1-3))^2= approx 1/(2^4)
Hence B.
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If 2^4x = 3,600, what is the value of (2^1-x)^2 ?  [#permalink]

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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

pushpitkc hello there, can you please tell what am i doing wrong in my solution and why i am doing it wrong so we have $$2^{4x} = 3,600$$ (the first thing that came to my mind is that i need to bring both sides to the same base) so here is what i did

$$2^{4x} = 36*10^2$$ (now break down 36 into primes which is $$3^2*2^2$$ see below in next step)

$$2^{4x} = 3^2*2^2*10^2$$ ( here since i want to have the same bases of 2 i do following) turn $$3^2$$ into $$2^3$$ and $$10^2$$ into $$2^{10}$$(see below)

$$2^{4x} = 2^2*2^2*2^{10}$$

$$2^{4x} = 2^{14}$$[ now equate bases $$4x = 14$$

x= $$\frac{14}{4}$$ --> $$\frac{7}{2}$$ now what question in conclusion: shoudldnt we always equate bases in similrar question as i did in the above solution:)

thank you Manager  S
Joined: 22 Jan 2014
Posts: 169
WE: Project Management (Computer Hardware)
Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ?  [#permalink]

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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

2^4x = 3600
taking log both sides
4x log 2 = log 2^4 + log 3^2 + log 5^2
or log 3^2 + log 5^2 = 4 log 2 (x-1)
or log 3 + log 5 = 2 log 2 (x-1)
=> (2^(1-x))^2 = 1/15
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If 2^4x = 3,600, what is the value of (2^1-x)^2 ?  [#permalink]

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1
dave13 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

pushpitkc hello there, can you please tell what am i doing wrong in my solution and why i am doing it wrong so we have $$2^{4x} = 3,600$$ (the first thing that came to my mind is that i need to bring both sides to the same base) so here is what i did

$$2^{4x} = 36*10^2$$ (now break down 36 into primes which is $$3^2*2^2$$ see below in next step)

$$2^{4x} = 3^2*2^2*10^2$$ ( here since i want to have the same bases of 2 i do following) turn $$3^2$$ into $$2^3$$ and $$10^2$$ into $$2^{10}$$(see below)

$$2^{4x} = 2^2*2^2*2^{10}$$

$$2^{4x} = 2^{14}$$[ now equate bases $$4x = 14$$

x= $$\frac{14}{4}$$ --> $$\frac{7}{2}$$ now what question in conclusion: shoudldnt we always equate bases in similrar question as i did in the above solution:)

thank you Hi dave13

You equate bases whenever it is possible. In cases like these, where
bases can't be equated you will have another options to solve the problem

The reason what you have done is wrong is because
$$2^10 = 1024$$, whereas $$10^2 = 100$$
$$2^3 = 8$$, whereas $$3^2 = 9$$
How can the expressions where you made these changes be equal??

Since we have been asked to find the value of $$2^{(1-x)^2}$$
It can be further simplified as $$2^{2 - 2x}$$ which is nothing but $$\frac{2^2}{2^{2x}}$$

Hope this helps you!
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Joined: 07 Apr 2018
Posts: 101
Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ?  [#permalink]

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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

To find: (2^(1-x))^2
=> 2^(2-2x) = 4/ 2^2x ........................................(1)

Given: 2^4x= 3600 = 2^4 * 3^2 * 5^2
taking square root, we get
2^2x= 2^2 * 3 * 5..................................................(2)

Putting the value of 2^2x from eqn(2) to eqn(1), we get

4/2^2x = 4/(4 * 3 * 5) = 1/15

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Joined: 12 Sep 2015
Posts: 4055
Re: If 2^4x = 3,600, what is the value of (2^1-x)^2 ?  [#permalink]

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1
Top Contributor
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

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

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

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

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