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2^x*4^(2x) = 8^y. Which of the following must be true?

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Bunuel
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2^x*4^(2x) = 8^y. Which of the following must be true? [#permalink] New post   28 Dec 2016, 11:06
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2^x*4^(2x) = 8^y. Which of the following must be true?

(A) 3x = y

(B) x = 3y

(C) y = (3/5)x

(D) x = (3/5)y

(E) 2x^2 = y
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D
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Alexey1989x
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Re: 2^x*4^(2x) = 8^y. Which of the following must be true? [#permalink] New post   28 Dec 2016, 15:12
2^x*4^2x=8^y
2^x*2^4x=2^3y
x+4x=3y
x=3/5y
Answer D.
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Abhishek009
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2^x*4^(2x) = 8^y. Which of the following must be true? [#permalink] New post   29 Dec 2016, 11:40
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Bunuel wrote:
\(2^x*4^{2x} = 8^y.\) Which of the following must be true?

(A) 3x = y

(B) x = 3y

(C) y = (3/5)x

(D) x = (3/5)y

(E) 2x^2 = y

\(2^x*2^{4x} = 2^{3y}\)

Or, \(2^{5x} = 2^{3y}\)

So, y = \(\frac{5x}{3}\) Or, \(x = \frac{3y}{5}\)

Hence, the correct answer must be (D) \(x = \frac{3y}{5}\)
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Re: 2^x*4^(2x) = 8^y. Which of the following must be true? [#permalink] New post   30 Dec 2016, 07:00
Abhishek009 wrote:
Bunuel wrote:
\(2^x*4^{2x} = 8^y.\) Which of the following must be true?

(A) 3x = y

(B) x = 3y

(C) y = (3/5)x

(D) x = (3/5)y

(E) 2x^2 = y

\(2^x*2^{4x} = 2^{3y}\)

Or, \(2^{5x} = 2^{3y}\)

So, y = \(\frac{5x}{3}\) Or, \(x = \frac{3y}{5}\)

Hence, the correct answer must be (D) \(x = \frac{3y}{5}\)


How did you re order \(2^{5x} = 2^{3y}\) in terms of x=
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Re: 2^x*4^(2x) = 8^y. Which of the following must be true? [#permalink] New post   12 Feb 2017, 05:01
We have, 2^x * 4^2x = 8^y
4 is actually 2^2
and 8 is actually 2^3.
Hence, we have, 2^x * 2^4x = 2^3y.
Now, x^a * x^b = x^(a+b).
Therefore, 2^(5x) = 2^(3y)
Hence, 5x=3y.
Hence, x=(3/5)y. ..... D.
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2^x*4^(2x) = 8^y. Which of the following must be true? [#permalink] New post   12 Feb 2017, 06:01
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Bunuel wrote:
2^x*4^(2x) = 8^y. Which of the following must be true?

(A) 3x = y

(B) x = 3y

(C) y = (3/5)x

(D) x = (3/5)y

(E) 2x^2 = y



Hey,


PFB the solution. :)

    • \(2^x*4^{(2x)} = 8^y\)

    • Applying \((a^b)^c = a^{bc}\), we get

      o \(2^x * 2^{(2*2x)} = 2^{3*y}\)

    • Applying \(a^b * a^c = a^{(b+c)}\)

      o \(2^{(x+4x)} = 2^{(3y)}\)

    • \(2^{5x} = 2^{3y}\)

Comparing both side we can say that –
    • \(5x = 3y\)

    • \(x = \frac{{3y}}{5}\)

• Correct Option : D

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Re: 2^x*4^(2x) = 8^y. Which of the following must be true? [#permalink] New post   18 Apr 2017, 04:02
Bunuel wrote:
2^x*4^(2x) = 8^y. Which of the following must be true?

(A) 3x = y

(B) x = 3y

(C) y = (3/5)x

(D) x = (3/5)y

(E) 2x^2 = y


I took 1:25 to solve though it should take max 60 seconds for average users

2^x*2^4x=2^3y
2^5x=2^3y
5x=3y
x=3/5*y
Choice:D
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Re: 2^x*4^(2x) = 8^y. Which of the following must be true? [#permalink]
18 Apr 2017, 04:02
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