2^x+2^x+2^x+2^x = 2^n : GMAT Problem Solving (PS)
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# 2^x+2^x+2^x+2^x = 2^n

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Manager
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12 Jan 2011, 21:59
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79% (01:18) correct 21% (00:08) wrong based on 14 sessions

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it can be rewritten:
$$4*2^x=2^n$$
$$4=2^2$$
then
$$2^2*2^x=2^n$$
we can write 2+x=n
so, x=n-2
(D)
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13 Jan 2011, 07:56
ulm wrote:
it can be rewritten:
$$4*2^x=2^n$$
$$4=2^2$$
then
$$2^2*2^x=2^n$$
we can write 2+x=n
so, x=n-2
(D)

D as well with the same reasoning
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13 Jan 2011, 09:00
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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20 Jan 2011, 05:29
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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20 Jan 2011, 07:21
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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18 Feb 2011, 14:02
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: 2^x+2^x+2^x+2^x = 2^n   [#permalink] 18 Feb 2011, 14:02
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