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Re: If f and g are both positive integers greater than 1 [#permalink]
25 Jul 2014, 10:13

Expert's post

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.

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