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

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Manager
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Re: 2^x+2^x+2^x+2^x = 2^n [#permalink] New post 12 Jan 2011, 21:59
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

80% (01:17) correct 20% (00:00) wrong based on 10 sessions
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)
[Reveal] Spoiler: OA
Joined: 31 Dec 1969
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Re: 2^x+2^x+2^x+2^x = 2^n [#permalink] New post 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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Re: 2^x+2^x+2^x+2^x = 2^n [#permalink] New post 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.

answer d
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Re: 2^x+2^x+2^x+2^x = 2^n [#permalink] New post 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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Re: 2^x+2^x+2^x+2^x = 2^n [#permalink] New post 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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Re: 2^x+2^x+2^x+2^x = 2^n [#permalink] New post 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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