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If 8^(n + 1) + 8^n = 36, then n =

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If 8^(n + 1) + 8^n = 36, then n =  [#permalink]

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New post 24 Jan 2018, 23:11
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (01:15) correct 31% (01:33) wrong based on 66 sessions

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Re: If 8^(n + 1) + 8^n = 36, then n =  [#permalink]

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New post 24 Jan 2018, 23:29
D

We know 2^3=8.

Also 36 can be split as 32+4 which are some powers of 2.

Now (2^3)^(n+1) + (2^3)^n =32 + 4

(8)^(n+1) + (8)^n = 8^(5/3) + 8^(2/3)

Hence n=2/3. We can check by n+1=5/3 which gives n=2/3 also holds true.


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Re: If 8^(n + 1) + 8^n = 36, then n =  [#permalink]

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New post 24 Jan 2018, 23:37
Bunuel wrote:
If 8^(n + 1) + 8^n = 36, then n =

A. 1/3
B. 1/2
C. 3/5
D. 2/3
E. 4/5


Let \(8^n = x\), \(9x = 36\) -->\(x = 4\)
\(n = 2/3.\)
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Re: If 8^(n + 1) + 8^n = 36, then n =  [#permalink]

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New post 25 Jan 2018, 08:23
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Bunuel wrote:
If 8^(n + 1) + 8^n = 36, then n =

A. 1/3
B. 1/2
C. 3/5
D. 2/3
E. 4/5

\(8^{n + 1} + 8^n = 36\)

Or, \(8^n*8 + 8^n = 36\)

Or, \(8^n(8 + 1) = 36\)

Or, \(8^n = 4\)

Or, \(2^{3n} = 2^2\)

Or, \(3n = 2\)

Or, \(n = \frac{2}{3}\), Answer will be (D)
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Re: If 8^(n + 1) + 8^n = 36, then n =  [#permalink]

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New post 25 Jan 2018, 10:09
[quote="Bunuel"]If 8^(n + 1) + 8^n = 36, then n =

8^n x 8 + 8^n = 36

8^n (8 + 1) = 4 x 9

8^n x 9 = 4 x 9

so 8^n = 4

8^1/3 = 2 so 8 ^ 2/3 = 2 x 2 = 4. So Answer is n = 2/3
Re: If 8^(n + 1) + 8^n = 36, then n = &nbs [#permalink] 25 Jan 2018, 10:09
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