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If f and g are both positive integers greater than 1

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If f and g are both positive integers greater than 1 [#permalink] New post 25 Jul 2014, 10:00
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If f and g are both positive integers greater than 1 and g^f = g^{(3f-6)}, what is the value of fg ?

(1) g^2 = 2g

(2) g=2
[Reveal] Spoiler: OA

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Last edited by Bunuel on 25 Jul 2014, 10:07, edited 1 time in total.
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Re: If f and g are both positive integers greater than 1 [#permalink] New post 25 Jul 2014, 10:13
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If f and g are both positive integers greater than 1 and g^f = g^{(3f-6)}, what is the value of fg ?

g^f = g^{(3f-6)} --> \frac{g^f}{g^{(3f-6)}}=1 --> g^{f-3f+6} =1 --> g^{6-2f}=1. Since g>1, then 6-2f=0 --> f=3. Thus to get the value of fg we need the value of g.

(1) g^2 = 2g --> g(g-2)=0 --> g=0 (discard as g>1) or g=2 --> fg=3*2=6. Sufficient.

(2) g=2. Sufficient.

Answer; D.
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Re: If f and g are both positive integers greater than 1 [#permalink] New post 25 Jul 2014, 17:41
Bunuel can you explain the theory by dropping the g because g>1 and setting it equal to zero ?
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Re: If f and g are both positive integers greater than 1 [#permalink] New post 26 Jul 2014, 01:05
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bankerboy30 wrote:
Bunuel can you explain the theory by dropping the g because g>1 and setting it equal to zero ?


For a^n to be 1, either a should be 1 or n should be 0:

a^0=1: any nonzero number to the power of 0 is 1.
1^n=1: the integer powers of one are one.

Check here for more: exponents-and-roots-on-the-gmat-tips-and-hints-174993.html

Hope it helps.
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Re: If f and g are both positive integers greater than 1   [#permalink] 26 Jul 2014, 01:05
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