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

3

Expert Reply

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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

❑ \(\frac{a}{7}\)

❑ \(\frac{b}{2}\)

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

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

AND

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

Hope you spot the gist of the problem.

Regards

Re: 3^2a 11^b
[#permalink]
27 Aug 2021, 21:37

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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