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TAGS: Founder  Joined: 18 Apr 2015
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Expert's post 00:00

Question Stats: 81% (01:13) correct 18% (01:35) wrong based on 77 sessions Director Joined: 03 Sep 2017
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Here there is a missing OA! VP Joined: 20 Apr 2016
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WE: Engineering (Energy and Utilities)
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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

❑ $$\frac{a}{7}$$

❑ $$\frac{b}{2}$$

[Reveal] Spoiler: 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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Intern Joined: 14 Jun 2018
Posts: 36
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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

❑ $$\frac{a}{7}$$

❑ $$\frac{b}{2}$$

[Reveal] Spoiler: 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?
Founder  Joined: 18 Apr 2015
Posts: 13940
GRE 1: Q160 V160 Followers: 316

Kudos [?]: 3690 , given: 12953

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