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

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by Ian Stewart » Sat Mar 02, 2019 4:07 am
2^(4x) = 3600, so (2^2)^2x = 3600, and 4^(2x) = 3600. Taking square roots, 4^x = 60.

We want to find the value of (2^(1-x))^2 = (2^2)^(1-x) = 4^(1-x) = 4^1 * 4^(-x)

Since 4^x = 60, 4^(-x) is equal to 1/60, so 4^1 * 4^(-x) = 4 * (1/60) = 4/60 = 1/15
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by Ian Stewart » Sat Mar 02, 2019 4:10 am
Alternatively:

2^(4x) = 3600
2^(2x) = 60
2^x = √60

So

(2^(1-x))^2 = (2 / 2^x)^2 = (2/√60)^2 = 4/60 = 1/15
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by GMATGuruNY » Sat Mar 02, 2019 4:30 am
BTGmoderatorLU wrote:Source: Official Guide

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

A. \(-\frac{1}{15}\)
B. \(\frac{1}{15}\)
C. \(\frac{3}{10}\)
D. \(-\frac{3}{10}\)
E. \(1\)
\((2^{(1-x)})^2\) = \(2^{2-2x}\) = \(2^2/2^{2x}\) = \(4/2^{2x}\)

We need to know the value of \(2^{2x}\):
\(2^{4x}=3,600\)
\((2^{2x})^2=3,600\)
\(2^{2x}= 60\)

Substituting \(2^{2x}= 60\) into \(4/2^{2x}\), we get:
4/60 = 1/15

The correct answer is B.
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by Scott@TargetTestPrep » Wed Mar 06, 2019 6:55 pm
BTGmoderatorLU wrote:Source: Official Guide

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

A. \(-\frac{1}{15}\)
B. \(\frac{1}{15}\)
C. \(\frac{3}{10}\)
D. \(-\frac{3}{10}\)
E. \(1\)

The OA is B
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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