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# If 2^x + 2^x + 2^x + 2^x = 2^n, what is x in terms of n?

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If 2^x + 2^x + 2^x + 2^x = 2^n, what is x in terms of n? [#permalink]

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12 Jan 2011, 22:59
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If $$2^x + 2^x + 2^x + 2^x = 2^n$$, what is x in terms of n?

A. n/4

B. 4n

C. 2n

D. n - 2

E. n + 2
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 May 2017, 13:35, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: If 2^x + 2^x + 2^x + 2^x = 2^n, what is x in terms of n? [#permalink]

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13 Jan 2011, 10:00
2^x + 2^x + 2^x + 2^x = 4 * 2^x = 2^2 * 2^x = 2^(2+x)
so , if 2^(2+x)= 2^n then 2+x=n so x=n-2.

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Re: If 2^x + 2^x + 2^x + 2^x = 2^n, what is x in terms of n? [#permalink]

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20 Jan 2011, 06:29
Yep D
4(2^x)=2^n
2^2(2^x)=2^n
2^(x+2)=2^n
x+2=n
x=n-2

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Re: If 2^x + 2^x + 2^x + 2^x = 2^n, what is x in terms of n? [#permalink]

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20 Jan 2011, 08:21
I to am with the algebraic approach for arriving at the solution.

But if in the heat of things we forget $$a ^ m * a ^ n = a ^ {(m+n)}$$ we can substitute for x and solve

$$2^x + 2^x + 2^x + 2^x = 2^n$$

Substitute x = 1

$$2^1 + 2^1 + 2^1 + 2^1 = 2^n$$

$$8 = 2^n$$

$$n = 3$$

$$x = 1 & n = 3$$
$$x = 1 = n - 2$$

D
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Re: If 2^x + 2^x + 2^x + 2^x = 2^n, what is x in terms of n? [#permalink]

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18 Feb 2011, 15:02
u can also plug x=0 and u get n=2.
than u can c on the answers
n-2 = x

2-2=0. finish...
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Re: If 2^x + 2^x + 2^x + 2^x = 2^n, what is x in terms of n? [#permalink]

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20 May 2017, 05:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If 2^x + 2^x + 2^x + 2^x = 2^n, what is x in terms of n? [#permalink]

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20 May 2017, 13:27
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bumpbot , the question is missing
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Re: If 2^x + 2^x + 2^x + 2^x = 2^n, what is x in terms of n? [#permalink]

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20 May 2017, 13:38
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genxer123 wrote:
bumpbot , the question is missing

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If 2^x + 2^x + 2^x + 2^x = 2^n, what is x in terms of n? [#permalink]

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20 May 2017, 16:11
ulm wrote:
If $$2^x + 2^x + 2^x + 2^x = 2^n$$, what is x in terms of n?

A. n/4

B. 4n

C. 2n

D. n - 2

E. n + 2

4*2^x=2^n
2^2*2^x=2^n
2^2*2^1=2^3
x=1
n=3
x=n-2
D
If 2^x + 2^x + 2^x + 2^x = 2^n, what is x in terms of n?   [#permalink] 20 May 2017, 16:11
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