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If 8x=2^y, what is the value of x, in terms of y?

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Math Revolution GMAT Instructor
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If 8x=2^y, what is the value of x, in terms of y?  [#permalink]

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New post 06 Oct 2017, 02:44
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[GMAT math practice question]

If \(8x=2^y\), what is the value of x, in terms of y?

A. \(x=2^{3y-2}\)
B. \(x=4y\)
C. \(x=4^{y-2}\)
D. \(x=2^{y-3}\)
E. \(x=2y\)

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Re: If 8x=2^y, what is the value of x, in terms of y?  [#permalink]

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New post 06 Oct 2017, 04:26
MathRevolution wrote:
[GMAT math practice question]

If \(8x=2^y\), what is the value of x, in terms of y?

A. \(x=2^{3y-2}\)
B. \(x=4y\)
C. \(x=4^{y-2}\)
D. \(x=2^{y-3}\)
E. \(x=2y\)


\(8x=2^y\) ==> \(2^3x=2^y\) ==> \(x=2^y/(2^3)\) ==>\(x=2^{y-3}\)

Ans - D
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Re: If 8x=2^y, what is the value of x, in terms of y?  [#permalink]

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New post 08 Oct 2017, 18:05
=>
\(8x = 2^y ⬄ 2^3x = 2^y ⬄ x = 2^{y-3}\)

Answer : D
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Re: If 8x=2^y, what is the value of x, in terms of y?  [#permalink]

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New post 17 Jul 2018, 08:36
Top Contributor
MathRevolution wrote:
[GMAT math practice question]

If \(8x=2^y\), what is the value of x, in terms of y?

A. \(x=2^{3y-2}\)
B. \(x=4y\)
C. \(x=4^{y-2}\)
D. \(x=2^{y-3}\)
E. \(x=2y\)


Another approach is to find some values of x and y that satisfy the given equation 8x = 2^y
One solution that works is x = 1 and y = 3, since 8(1) = 2^3
Now take each answer choice and replace x and y with 1 and 3 respectively and see which one yields a true equation:

A. 1 = 2^[3(3) - 2] Not true. ELIMINATE
B. 1 = 4(3) Not true. ELIMINATE
C. 1 = 4^(3 - 2) Not true. ELIMINATE
D. 1 = 2^(3 - 3) True. KEEP!
E. 1 = 2(3) Not true. ELIMINATE

Answer: D

Cheers,
Brent
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Re: If 8x=2^y, what is the value of x, in terms of y?  [#permalink]

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New post 19 Jul 2018, 16:57
MathRevolution wrote:
[GMAT math practice question]

If \(8x=2^y\), what is the value of x, in terms of y?

A. \(x=2^{3y-2}\)
B. \(x=4y\)
C. \(x=4^{y-2}\)
D. \(x=2^{y-3}\)
E. \(x=2y\)


Simplifying, we have:

2^3 * x = 2^y

x = 2^y / 2^3

x = 2^(y - 3)

Answer: D
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Re: If 8x=2^y, what is the value of x, in terms of y? &nbs [#permalink] 19 Jul 2018, 16:57
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