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Reni
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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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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lawiniecke
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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Reni
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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Reni
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

Answer: B

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(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
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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?
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levin343
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?

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
Attachments

1000032702.jpg
1000032702.jpg [ 3.79 MiB | Viewed 12033 times ]

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