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# If 3^27^x = 27^3^x , then x is equal to

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Senior Manager
Joined: 24 Apr 2016
Posts: 333
If 3^27^x = 27^3^x , then x is equal to  [#permalink]

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10 Mar 2017, 13:08
4
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:01) correct 39% (01:55) wrong based on 46 sessions

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If 3^27^x = 27^3^x , then x is equal to

A.−1

B. 1/2

C.1

D.2

E.-1/2
Senior Manager
Joined: 14 Oct 2015
Posts: 250
GPA: 3.57
If 3^27^x = 27^3^x , then x is equal to  [#permalink]

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11 Mar 2017, 04:54
quantumliner wrote:
If 3^27^x = 27^3^x , then x is equal to

A.−1

B. 1/2

C.1

D.2

E.-1/2

I scratched my head a lot since I was rusty on these questions and had to view the answer first. I am partly convinced I have found the right path but would welcome any correction

RHS can be rewritten as

(3^3)^3^x

= 3 ^ (3.3^x)

equating powers of matching base from both LHS and RHS.

$$27^x = 3.3^x$$

27^x = 3^(x+1)

LHS can be rewritten.

(3^3)^x= 3^(x+1)

3^3x = 3^(x+1)

equating powers of matching base again

$$3x = x + 1$$

$$2x = 1$$

$$x = 1/2$$
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Intern
Joined: 13 May 2014
Posts: 5
Schools: ISB '16
Re: If 3^27^x = 27^3^x , then x is equal to  [#permalink]

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11 Mar 2017, 07:41
You lost me while solving RHS when you stated that 27^x = 3^(x+1).

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Senior Manager
Joined: 14 Oct 2015
Posts: 250
GPA: 3.57
Re: If 3^27^x = 27^3^x , then x is equal to  [#permalink]

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11 Mar 2017, 07:52
On RHS, we had $$3 x 3^x$$ which is same as $$3^1 x 3^x$$ and when base is same we just add the powers so it becomes 3^x+1

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Senior Manager
Joined: 06 Dec 2016
Posts: 250
Re: If 3^27^x = 27^3^x , then x is equal to  [#permalink]

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11 Mar 2017, 20:23
Can VeritasPrepKarishma or Bunuel please explain this one to me step by step.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8386
Location: Pune, India
Re: If 3^27^x = 27^3^x , then x is equal to  [#permalink]

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11 Mar 2017, 21:15
1
matthewsmith_89 wrote:
Can VeritasPrepKarishma or Bunuel please explain this one to me step by step.

Here is the step by step process:

Attachment:

IMG_7211.JPG [ 1.56 MiB | Viewed 1337 times ]

Note: When two numbers with the same base are multiplied, their exponents get added.
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Re: If 3^27^x = 27^3^x , then x is equal to &nbs [#permalink] 11 Mar 2017, 21:15
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