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If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive

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If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive [#permalink] New post 27 May 2012, 09:21
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75% (01:28) correct 25% (03:38) wrong based on 0 sessions
If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive integers, what is the value of a?

A. 22
B. 11
C. 9
D. 6
E. 3
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Re: If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive [#permalink] New post 28 May 2012, 00:32
macjas wrote:
If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive integers, what is the value of a?

A. 22
B. 11
C. 9
D. 6
E. 3


18^a*9^{3a-1}=2^3*3^b --> (2^a*3^{2a})*3^{6a-2}=2^3*3^b --> 2^a*3^{8a-2}=2^3*3^b --> since both a and b are positive integers then the powers of 2 on both sides must be equal: a=3.

Answer: E.
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Re: If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive   [#permalink] 28 May 2012, 00:32
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If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive

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