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

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

by VJesus12 » Tue Jul 17, 2018 12:59 am

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If 8x=2^y what is the value of x, in terms of y? $$A.\ x=2^{3y-2}\ $$ $$B.\ x=4y$$ $$C.\ x=4^{y-2}$$ $$D.\ x=2^{y-3}$$ $$E.\ x=2y$$ The OA is the option D.

How can I get the option D from the given equation? Could anyone show me a good approach? Please.
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by Vincen » Tue Jul 17, 2018 2:04 am
VJesus12 wrote:If 8x=2^y what is the value of x, in terms of y? $$A.\ x=2^{3y-2}\ $$ $$B.\ x=4y$$ $$C.\ x=4^{y-2}$$ $$D.\ x=2^{y-3}$$ $$E.\ x=2y$$ The OA is the option D.

How can I get the option D from the given equation? Could anyone show me a good approach? Please.
Hello Vjesus12.

Let's take a look at your question. We need to solve for x the equation $$8x=2^y.$$ From this, we can get $$x=\frac{2^y}{8}$$ $$x=\frac{2^y}{2^3}$$ $$x=2^{y-3}.$$ And so, the correct answer is the option D.

I hope it is clear enough. <i class="em em-smiley"></i>
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by Brent@GMATPrepNow » Tue Jul 17, 2018 6:00 am
VJesus12 wrote:If 8x=2^y what is the value of x, in terms of y? $$A.\ x=2^{3y-2}\ $$ $$B.\ x=4y$$ $$C.\ x=4^{y-2}$$ $$D.\ x=2^{y-3}$$ $$E.\ x=2y$$ The OA is the option D.

How can I get the option D from the given equation? Could anyone show me a good approach? Please.
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
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Thu Jul 19, 2018 4:20 pm
VJesus12 wrote:If 8x=2^y what is the value of x, in terms of y? $$A.\ x=2^{3y-2}\ $$ $$B.\ x=4y$$ $$C.\ x=4^{y-2}$$ $$D.\ x=2^{y-3}$$ $$E.\ x=2y$$ The OA is the option D.
Simplifying, we have:

2^3 * x = 2^y

x = 2^y / 2^3

x = 2^(y - 3)

Answer: D

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