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

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Joined: 02 Sep 2009
Posts: 58313
If 8^(n + 1) + 8^n = 36, then n =  [#permalink]

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24 Jan 2018, 23:11
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15% (low)

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77% (01:16) correct 23% (01:53) wrong based on 95 sessions

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

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

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

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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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24 Jan 2018, 23:37
1
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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25 Jan 2018, 08:23
4
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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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
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Re: If 8^(n + 1) + 8^n = 36, then n =  [#permalink]

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05 Jul 2019, 22:14
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Re: If 8^(n + 1) + 8^n = 36, then n =   [#permalink] 05 Jul 2019, 22:14
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# If 8^(n + 1) + 8^n = 36, then n =

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