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# If 16^x/4^y = 64, which of the following must be true?

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Joined: 02 Sep 2009
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If 16^x/4^y = 64, which of the following must be true?  [#permalink]

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16 Feb 2017, 02:41
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Difficulty:

15% (low)

Question Stats:

88% (01:25) correct 13% (01:28) wrong based on 94 sessions

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If 16^x/4^y = 64, which of the following must be true?

A. 4x+6=2y
B. 2x−y=6
C. y−2x=3
D. y=2x−3
E. 2y−x=3

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Re: If 16^x/4^y = 64, which of the following must be true?  [#permalink]

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16 Feb 2017, 02:55
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1
Bunuel wrote:
If 16^x/4^y = 64, which of the following must be true?

A. 4x+6=2y
B. 2x−y=6
C. y−2x=3
D. y=2x−3
E. 2y−x=3

$$16^x/4^y = 64$$
$$4^{2x}/4^y = 4^3$$
$$4^{2x-y} = 4^3$$
2x-y=3
y=2x-3

Hence Option D is correct.
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Re: If 16^x/4^y = 64, which of the following must be true?  [#permalink]

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16 Feb 2017, 06:07
16 = 2^4
16^x = 2^4x

4 = 2^2
4^y = 2^2y

2^4x / 2^2y = 2^4x-2y

64 = 2^6

2^4x-2y = 2^6

4x-2y = 6
2x-y = 3

y=2x−3 (Choice D)
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Re: If 16^x/4^y = 64, which of the following must be true?  [#permalink]

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16 Feb 2017, 07:10
Bunuel wrote:
If 16^x/4^y = 64, which of the following must be true?

A. 4x+6=2y
B. 2x−y=6
C. y−2x=3
D. y=2x−3
E. 2y−x=3

$$\frac{16^x}{4^y} = 64$$

Or, $$\frac{2^{4x}}{2^{2y}} = 2^6$$

Or, $$2^{ 4x - 2y } = 2^6$$

Or, $$4x - 2y = 6$$

Or, $$2x - y = 3$$

Or, $$y = 2x - 3$$

Answer will be (D) $$y = 2x - 3$$
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Re: If 16^x/4^y = 64, which of the following must be true?  [#permalink]

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21 Feb 2017, 09:20
1
Bunuel wrote:
If 16^x/4^y = 64, which of the following must be true?

A. 4x+6=2y
B. 2x−y=6
C. y−2x=3
D. y=2x−3
E. 2y−x=3

Let’s simplify each component of the given equation:

16^x = 2^4x

4^y = 2^2y

64 = 2^6

So we have:

(2^4x)/(2^2y) = 2^6

2^(4x - 2y) = 2^6

4x - 2y = 6

4x - 6 = 2y

y = 2x - 3

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Re: If 16^x/4^y = 64, which of the following must be true?  [#permalink]

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11 Jun 2018, 13:57
Bunuel wrote:
If 16^x/4^y = 64, which of the following must be true?

A. 4x+6=2y
B. 2x−y=6
C. y−2x=3
D. y=2x−3
E. 2y−x=3

it's given ,

$$16^x$$/$$4^y$$ =64

$$([m]4^2$$)^x[/m] / $$4^y$$ = $$4^3$$

$$4^{2x}$$/$$4^Y$$= 4^3
$$4^{2x-y}$$ = $$4^3$$
2x-y =3
y = 2x -3

Thus the best answer is D.
Re: If 16^x/4^y = 64, which of the following must be true? &nbs [#permalink] 11 Jun 2018, 13:57
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