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If 2x+2x+2x+2x=2a, x=?

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Math Revolution GMAT Instructor
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25 Jan 2017, 05:15
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If $$2^x+2^x+2^x+2^x=2^a$$, x=?

A. a-2
B. a+2
C. 2-a
D. 2a
E. a-4

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" GMAT Club Legend Joined: 12 Sep 2015 Posts: 4007 Location: Canada Re: If 2x+2x+2x+2x=2a, x=? [#permalink] Show Tags 25 Jan 2017, 07:56 2 Top Contributor MathRevolution wrote: If $$2^x+2^x+2^x+2^x=2^a$$, x=? A. a-2 B. a+2 C. 2-a D. 2a E. a-4 Nice question! We need to recognize here that we first need to simplify the left side of the equation. We are adding 2^x FOUR times, which is the same as (4)2^x So... 2^x + 2^x + 2^x + 2^x = 2^a (4)(2^x) = 2^a (2^2)(2^x) = 2^a [I rewrote 4 as 2^2] 2^(x+2) = 2^a [applied the product law for exponents] Since we have the same base of 2 on each side of the equation, we can conclude that the exponents are equal. So.... x+2 = a Subtract 2 from both sides to get: x = a-2 Answer: RELATED VIDEO _________________ Test confidently with gmatprepnow.com VP Joined: 05 Mar 2015 Posts: 1003 Re: If 2x+2x+2x+2x=2a, x=? [#permalink] Show Tags 25 Jan 2017, 12:36 MathRevolution wrote: If $$2^x+2^x+2^x+2^x=2^a$$, x=? A. a-2 B. a+2 C. 2-a D. 2a E. a-4 substitute x=2 in 2^x+2^x+2^x+2^x 2^x+2^x+2^x+2^x= 16 = 2^4 = 2^a thus a=4 & x=2 check with options which satisfies x=2 when a=4 only option A satisfies x= 2 Hence Ans A Manager Joined: 03 Oct 2013 Posts: 77 Re: If 2x+2x+2x+2x=2a, x=? [#permalink] Show Tags 25 Jan 2017, 13:08 4*(2^x) = (2^a) => (2^2)X(2^x) = 2^a => 2^(x+2) = 2^a => x+2 = a => x = a-2 _________________ P.S. Don't forget to give Kudos on the left if you like the solution Current Student Status: Entering into the MBA world... Joined: 17 Mar 2016 Posts: 37 Location: Saudi Arabia Concentration: General Management, Strategy Schools: Alberta"19 (A$)
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25 Jan 2017, 22:14
There are FOUR 2s with power X, so they would add to make
4*(2^)x = (2)^a
since 4=2^2
Therefore, (2)^2 *(2)^x = (2)^a
which results in;
(2)^(2+x) = (2)^a
=> x+2=a
x=a-2
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25 Jan 2017, 23:50
easy one, and thank you, GMATPrepNow
Math Revolution GMAT Instructor
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27 Jan 2017, 04:21
==> From $$2^x+2^x+2^x+2^x=(1+1+1+1)2^x=4(2^x)=2^22^x=2^2^+^x=2^a$$, you get $$2+x=a, x=a-2$$.

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30 Jan 2017, 17:58
MathRevolution wrote:
If $$2^x+2^x+2^x+2^x=2^a$$, x=?

A. a-2
B. a+2
C. 2-a
D. 2a
E. a-4

Keep in mind that in the first step we are ADDING the four terms on the left.

2^x + 2^x + 2^x + 2^x = 2^a

4(2^x) = 2^a

(2^2)(2^x) = 2^a

2^(2 + x) = 2^a

Because we have equal bases, we can equate the exponents:

2 + x = a

x = a - 2

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31 Jan 2017, 16:09
2^x ( 4 ) = 2^a
2^x 2^2 = 2^a
2^x+2 = 2^a
x + 2 = a
x = a - 2
A
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19 Jan 2019, 23:01
MathRevolution wrote:
If $$2^x+2^x+2^x+2^x=2^a$$, x=?

A. a-2
B. a+2
C. 2-a
D. 2a
E. a-4

$$2^x+2^x+2^x+2^x=2^a$$

4 *$$2^x = 2^ a$$

$$2^{x+2} = 2^a$$

x = a-2

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Re: If 2x+2x+2x+2x=2a, x=?   [#permalink] 19 Jan 2019, 23:01
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