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3^2a 11^b
[#permalink]
07 Aug 2017, 03:27

3

Expert Reply

Question Stats:

If \(3^{2a}\)\(11^b\)= \(27^{4x}\) \(33^{2x}\) then x must equal which of the following ?

Indicate all that apply.

❑ 2a

❑ 2b

❑ 7a - 2b

❑ \(\frac{a}{7}\)

❑ \(\frac{b}{2}\)

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Re: 3^2a 11^b
[#permalink]
24 Sep 2017, 07:32

2

Carcass wrote:

If \(3^{2a}\)\(11^b\)= \(27^{4x}\) \(33^{2x}\) then x must equal which of the following ?

Indicate all that apply.

❑ 2a

❑ 2b

❑ 7a - 2b

❑ \(\frac{a}{7}\)

❑ \(\frac{b}{2}\)

Indicate all that apply.

❑ 2a

❑ 2b

❑ 7a - 2b

❑ \(\frac{a}{7}\)

❑ \(\frac{b}{2}\)

Show: :: OA

Here given

\(3^{2a}\)\(11^b\)= \(27^{4x}\) \(33^{2x}\)

\(3^{2a}\)\(11^b\) = \(3^{12x}\) \(3^{2x}\) \(11^{2x}\) (Since \(27^{4x}\) = \({3^{(3x)}}^{4}\) = \(3^{12x}\))

or \(3^{2a}\)\(11^b\) = \(3^{14x}\) \(11^{2x}\)

Since prime bases are same, the exponents must also be equal.

14x = 2a,

or x= \(\frac{2}{14}\)

or a =\(\frac{a}{7}\)

And 2x = b, or x= \(\frac{b}{2}\)

Therefore only choices (D) and (E) must be true

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Re: 3^2a 11^b
[#permalink]
08 Jul 2018, 08:19

pranab01 wrote:

Carcass wrote:

If \(3^{2a}\)\(11^b\)= \(27^{4x}\) \(33^{2x}\) then x must equal which of the following ?

Indicate all that apply.

❑ 2a

❑ 2b

❑ 7a - 2b

❑ \(\frac{a}{7}\)

❑ \(\frac{b}{2}\)

Indicate all that apply.

❑ 2a

❑ 2b

❑ 7a - 2b

❑ \(\frac{a}{7}\)

❑ \(\frac{b}{2}\)

Show: :: OA

Here given

\(3^{2a}\)\(11^b\)= \(27^{4x}\) \(33^{2x}\)

\(3^{2a}\)\(11^b\) = \(3^{12x}\) \(3^{2x}\) \(11^{2x}\) (Since \(27^{4x}\) = \({3^{(3x)}}^{4}\) = \(3^{12x}\))

or \(3^{2a}\)\(11^b\) = \(3^{14x}\) \(11^{2x}\)

Since prime bases are same, the exponents must also be equal.

14x = 2a,

or x= \(\frac{2}{14}\)

or a =\(\frac{a}{7}\)

And 2x = b, or x= \(\frac{b}{2}\)

Therefore only choices (D) and (E) must be true

I know that one base equal to another will have the same exponent, but here we have two different bases. How that could be true to equate them as you did?

Re: 3^2a 11^b
[#permalink]
08 Jul 2018, 09:51

Expert Reply

Actuallly

\(3^{2a}= 3^{14x}\)

AND

\(11^b = 11^{2x}\)

Hope you spot the gist of the problem.

Regards

_________________

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ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides

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Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)

How is the GRE Score Calculated -The Definitive Guide (2021)

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\(3^{2a}= 3^{14x}\)

AND

\(11^b = 11^{2x}\)

Hope you spot the gist of the problem.

Regards

_________________

GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ

Search GRE Specific Questions | Download Vault

Posting Rules: QUANTITATIVE | VERBAL

FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)

Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:

ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides

3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection

Books: All GRE Best Books

Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)

How is the GRE Score Calculated -The Definitive Guide (2021)

Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)

Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021)

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