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If 8^x = 2^12, what is x?

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by M7MBA » Fri Apr 20, 2018 2:25 am

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Answers

A

B

C

D

E

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Difficulty—

If 8^x = 2^12, what is x?

A. 2
B. 3
C. 4
D. 5
E. 6

The OA is the option C.

What is the fastest way to solving this PS question? I would appreciate any help.
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by Brent@GMATPrepNow » Fri Apr 20, 2018 5:20 am
M7MBA wrote:If 8^x = 2^12, what is x?

A. 2
B. 3
C. 4
D. 5
E. 6
We need to rewrite the powers with the SAME BASES.
In this case, we can rewrite them with a common base of 2

Given: If 8^x = 2^12, what is x?
Rewrite 8 as 2³ to get: (2³)^x = 2^12
Apply Power of a Power rule to get: 2^(2x) = 2^12
So, we can conclude that: 2x =12
Solve: x = 6

Answer: 6

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Brent
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by Jeff@TargetTestPrep » Mon Apr 23, 2018 4:50 pm
M7MBA wrote:If 8^x = 2^12, what is x?

A. 2
B. 3
C. 4
D. 5
E. 6
If we have equal bases, then we can equate the exponents. Since 8 = 2^3, we see that 8^x = (2^3)^x = 2^3x. Thus, we have:

2^(3x) = 2^12

3x = 12

x = 4

Answer: C

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by [email protected] » Mon Apr 23, 2018 7:41 pm
Hi All,

We're told that 8^X = 2^12. We're asked for the value of X. This question can be solved in a number of different ways - depending on how you choose to do the math. Sometimes how you choose to "see" a GMAT question can give you a significant 'shortcut' in solving that question.

We know that 2^12 is just a bunch of 2s multiplied together (twelve 2s in fact). If we take three of those 2s and multiply them, we get (2)(2)(2) = 8. Since there are twelve 2s, we can rewrite THAT large calculation four 'trios' of 8....(8)(8)(8)(8). This is 8^4, so X=4.

Final Answer: C

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Rich
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