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

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Math Expert
Joined: 02 Sep 2009
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2^x*4^(2x) = 8^y. Which of the following must be true?  [#permalink]

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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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Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: 2^x*4^(2x) = 8^y. Which of the following must be true?  [#permalink]

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28 Dec 2016, 15:12
2^x*4^2x=8^y
2^x*2^4x=2^3y
x+4x=3y
x=3/5y
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2^x*4^(2x) = 8^y. Which of the following must be true?  [#permalink]

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29 Dec 2016, 11:40
1
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]

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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]

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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]

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12 Feb 2017, 06:01
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

Thanks,
Saquib
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Re: 2^x*4^(2x) = 8^y. Which of the following must be true?  [#permalink]

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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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Target#01 Q45,V20--April End

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