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Given that (3)^(a-b) = 1/81

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Given that (3)^(a-b) = 1/81 [#permalink] New post 30 Aug 2016, 02:50
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Given that \((3)^{(a-b)} = \frac{1}{81}\)

Quantity A
Quantity B
a
b



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


Please clear my doubt

there are 2 ways to see above problem
if we write (3)^(a-b) =3^a/3^b
then
3^a/3^b=1/81
a=0 and b=4

answer will be B


but similarly it can be seen as
(3)^(a-b) =3^(-4)
in this case a-b = -4
answer will be D
[Reveal] Spoiler: OA

Last edited by Carcass on 30 May 2018, 16:36, edited 5 times in total.
Added the OA
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Re: Very confused [#permalink] New post 30 Aug 2016, 03:21
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@Sonalika,
in your 2nd case a-b=-4 => b= a+4
therefore b>a

I would have solved this way

\(3^{a-b}\)= \(\frac{1}{81}\)
=> \(\frac{1}{3^{b-a}}\) = \(\frac{1}{81}\)
therefore b>a
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Re: Very confused [#permalink] New post 30 Aug 2016, 07:01
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B clearly. Took A as -5 and B as -1 or take A as 1 and B as 5.
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Re: Very confused [#permalink] New post 30 Aug 2016, 09:56
@phoenixio

thanks a lot, stupid of me...
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Re: Very confused [#permalink] New post 27 May 2018, 22:11
phoenixio wrote:
@Sonalika,
in your 2nd case a-b=-4 => b= a+4
therefore b>a

I would have solved this way

\(3^{a-b}\)= \(\frac{1}{81}\)
=> \(\frac{1}{3^{b-a}}\) = \(\frac{1}{81}\)
therefore b>a

Does this mean the answer is B? The question still carries the answer as D. I mean, it is intuitive that is a-b = -4, then a has to be less than b for it to be negative, right?
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Re: Given that (3)^(a-b) = 1/81 [#permalink] New post 28 May 2018, 01:46
@emike56

yup,you're right.
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Re: Given that (3)^(a-b) = 1/81 [#permalink] New post 29 May 2018, 19:15
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ste133 wrote:
@emike56

yup,you're right.


@carcass please change the answer to show B and not D. Otherwise, please provide the working solution that suggests its D.
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Re: Given that (3)^(a-b) = 1/81 [#permalink] New post 30 May 2018, 16:36
Expert's post
Fixed. Thank you.
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Re: Given that (3)^(a-b) = 1/81 [#permalink] New post 03 Jun 2018, 03:05
Okay, this is what I did. 1/81 = 1/(3^4)= 3^-4.
a-b=-4 which means B should be greater. Is this approach correct?
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Re: Given that (3)^(a-b) = 1/81 [#permalink] New post 04 Jun 2018, 06:03
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Correct approach :

3^(a-b) = 1/81
=3^(a-b) = 3^(-4)
comparing bases,
a-b = -4
hence, a = b - 4
which proves, a is 4 units smaller than b , no matter what.
Hence, B.

Cheers !
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Re: Given that (3)^(a-b) = 1/81 [#permalink] New post 05 Jun 2018, 17:26
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Answer: B

3^(a-b) = 1/81
3^(a-b) = 3^-4
a - b = -4
b - a = 4 and because b-a is positive, b is bigger than a.

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Re: Given that (3)^(a-b) = 1/81   [#permalink] 05 Jun 2018, 17:26
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