\(2^{4x} = 3600\)

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

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

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

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

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

Answer = B
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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).

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

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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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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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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