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# If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?

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If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ? [#permalink]

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17 Jan 2006, 12:06
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If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?

(A) 11/3
(B) 11/2
(C) 242
(D) 3^10
(E) 3^11 - 1
[Reveal] Spoiler: OA

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Last edited by Bunuel on 01 Sep 2014, 02:54, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ? [#permalink]

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17 Jan 2006, 13:13
C.

3^k + 3^k = 2.3^k = ((3^9)^3*9) - 3^k.
3.3^k = ((3^(9*27))

Thus, K+1 = 9*27 = 243.

Thus, k = 242.
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ? [#permalink]

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17 Jan 2006, 13:25
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3^k + 3^k = (3^9)^3^9 - 3^k

3*(3^k) = 3 ^ (9 * 3^9 ) = 3^(3^2 * 3^9) = 3^(3^11)

3^k+1 = 3^(3^11)

So k+1 = 3^11

So k = 3^11 -1

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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ? [#permalink]

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17 Jan 2006, 14:58
Its E

(3^11) -1

Giddi77,

Initially I got confused because answer choice E is 311 -1 instead of 3^11 -1.
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ? [#permalink]

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17 Jan 2006, 15:19
looks like giddi forgot the 3^11
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ? [#permalink]

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17 Jan 2006, 16:13
ps_dahiya wrote:
Its E

(3^11) -1

Giddi77,

Initially I got confused because answer choice E is 311 -1 instead of 3^11 -1.

Sir you are right! I have edited the question. It was an artifact of the copy and paste in the browser. Sorry about that.
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ? [#permalink]

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17 Jan 2006, 20:02
Yes got E after some struggle. Very nice question.
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ? [#permalink]

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17 Jan 2006, 22:41
yups E it is...
cud guess the value by just looking at the choices but took almost 4 min to get the real value
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ? [#permalink]

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24 Jan 2006, 07:29
Good question. Couldn't figure it out but learned a lot.

Thanks.
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ? [#permalink]

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31 Aug 2014, 00:53
chiragr wrote:
3^k + 3^k = (3^9)^3^9 - 3^k

3*(3^k) = 3 ^ (9 * 3^9 ) = 3^(3^2 * 3^9) = 3^(3^11)

3^k+1 = 3^(3^11)

So k+1 = 3^11

So k = 3^11 -1

Can you explain the LHS part of this equation? How did you get k+1 ?
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ? [#permalink]

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01 Sep 2014, 02:55
AkshayDavid wrote:
chiragr wrote:
If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?

(A) 11/3
(B) 11/2
(C) 242
(D) 3^10
(E) 3^11 - 1

3^k + 3^k = (3^9)^3^9 - 3^k

3*(3^k) = 3 ^ (9 * 3^9 ) = 3^(3^2 * 3^9) = 3^(3^11)

3^k+1 = 3^(3^11)

So k+1 = 3^11

So k = 3^11 -1

Can you explain the LHS part of this equation? How did you get k+1 ?

3*3^k = 3^(k+1).

Hope it's clear.
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ? [#permalink]

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01 Sep 2014, 20:09
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$$3^k + 3^k = (3^9)^{(3^9)} - 3^k$$

$$3 * 3^k = 3^{(3^2 * 3^9)}$$

$$3^{k+1} = 3^{(3^{11})}$$

Equating the powers as bases are same

$$k + 1 = 3^{11}$$

$$k = 3^{11} - 1$$

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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ? [#permalink]

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13 Sep 2015, 05:01
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ? [#permalink]

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29 Jan 2017, 05:26
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ? [#permalink]

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02 Feb 2017, 12:12
giddi77 wrote:
If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?

(A) 11/3
(B) 11/2
(C) 242
(D) 3^10
(E) 3^11 - 1

3^k + 3^k = (3^9)^(3^9) - 3^k

3^k + 3^k + 3^k = (3^9)^(3^9)

Note that on the left side, when we add 3^k to itself three times, we have 3(3^k).

3(3^k) = (3^9)^(3^9)

3^(k + 1) = 3^((3^2)(3^9))

3^(k + 1) = 3^(3^11)

Since the bases are equal, we can equate the exponents:

k + 1 = 3^11

k = 3^11 - 1

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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?   [#permalink] 02 Feb 2017, 12:12
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