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Re: If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ? [#permalink]

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12 Sep 2017, 07:39

Bunuel wrote:

If \(3^a – 3^{(a – 2)} = 8(3^{27})\), what is the value of 2a ?

A. 20 B. 25 C. 27 D. 29 E. 58

3^a - 3^(a-2) = 8(3^27) 3^a -(3^a/3^2) = 8(3^27) take lcm = 3^2 and then cross multiply the denominator (3^a)(3^2) - (3^a) = (3^2)(8)(3^27) take (3^a) common on LHS (3^a)[9-1] = (3^29)(8) cancel 8 on both sides (3^a) = (3^29) a= 29 2a = 58 option E
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If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ? [#permalink]

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Updated on: 24 Sep 2017, 06:30

RHS 8 can be written as (9-1) or (3²-1) 8(3²⁷)=(3²-1)X(3²⁷) =3²⁹-3²⁷ check answer choices. Start with easy one. let 2a=10 or a=5 plugin into LHS and check 3⁵-3³-Not correct let 2a=58 a=29 Plugin to LHS of the equation 3²⁹-3²⁷=LHS=correct=E

Originally posted by gps5441 on 24 Sep 2017, 06:27.
Last edited by gps5441 on 24 Sep 2017, 06:30, edited 1 time in total.

Re: If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ? [#permalink]

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24 Sep 2017, 06:29

RHS 8(3²⁷)=(3²-1)X(3²⁷) =3²⁹-3²⁷ check answer choices. Start with easy one. let 2a=10 or a=5 plugin into LHS and check 3⁵-3³-Not correct let 2a=58 a=29 Plugin to LHS of the equation 3²⁹-3²⁷=LHS=correct=E