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

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

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New post 16 Feb 2017, 03:41
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

87% (01:26) correct 13% (01:28) wrong based on 93 sessions

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

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New post 16 Feb 2017, 03:55
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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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New post 16 Feb 2017, 07:07
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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New post 16 Feb 2017, 08:10
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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New post 21 Feb 2017, 10:20
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

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

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New post 11 Jun 2018, 14:57
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.
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Re: If 16^x/4^y = 64, which of the following must be true? &nbs [#permalink] 11 Jun 2018, 14:57
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