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

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

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New post 10 Mar 2017, 12:08
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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
[Reveal] Spoiler: OA
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If 3^27^x = 27^3^x , then x is equal to [#permalink]

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New post 11 Mar 2017, 03:54
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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Re: If 3^27^x = 27^3^x , then x is equal to [#permalink]

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New post 11 Mar 2017, 06:41
You lost me while solving RHS when you stated that 27^x = 3^(x+1).

Could you please elaborate?

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Re: If 3^27^x = 27^3^x , then x is equal to [#permalink]

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New post 11 Mar 2017, 06:52
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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Re: If 3^27^x = 27^3^x , then x is equal to [#permalink]

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New post 11 Mar 2017, 19:23
Can VeritasPrepKarishma or Bunuel please explain this one to me step by step.
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Re: If 3^27^x = 27^3^x , then x is equal to [#permalink]

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New post 11 Mar 2017, 20:15
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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
IMG_7211.JPG [ 1.56 MiB | Viewed 731 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   [#permalink] 11 Mar 2017, 20:15
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