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If m=9^(x−1), then in terms of m, 3^(4x−2)

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If m=9^(x−1), then in terms of m, 3^(4x−2)  [#permalink]

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New post 03 Jun 2014, 13:20
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Question Stats:

60% (01:59) correct 40% (02:25) wrong based on 173 sessions

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If m=9^(x−1), then in terms of m, 3^(4x−2) must be which of the following?

A) m/3
B) 9m
C) 9m^2
D) m^2/3
E) m^2/9
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Re: If m=9^(x−1), then in terms of m, 3^(4x−2)  [#permalink]

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New post 03 Jun 2014, 13:38
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Re: If m=9^(x−1), then in terms of m, 3^(4x−2)  [#permalink]

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New post 03 Jun 2014, 19:44
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\(m = 9^{x-1}\)

\(m = 3^{2(x-1)}\)

\(m = 3^{2x - 2}\)

\(9m = 3^{2x}\)

Squaring both sides

\(81m^2 = 3^{4x}\)

Dividing both sides by 9

\(9m^2 = 3^{4x-2}\)

Answer = C
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Re: If m=9^(x−1), then in terms of m, 3^(4x−2)  [#permalink]

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New post 05 Nov 2016, 19:50
For this question I used a hypothetical value of x --> say x=3

m=9^(3-1) = 9^2 = 3^4

Plugging that same value of x into the new equation will give us --> 3^[(4)(3)-2]=3^10

The only choice where m can be transformed into 3^10 is C.
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Re: If m=9^(x−1), then in terms of m, 3^(4x−2)  [#permalink]

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New post 08 Jul 2018, 07:31
goodyear2013 wrote:
If m=9^(x−1), then in terms of m, 3^(4x−2) must be which of the following?

A) m/3
B) 9m
C) 9m^2
D) m^2/3
E) m^2/9

\(m=9^{x−1}\)

If \(x = 2 ; \ m = 9^1 = 9\)

Hence, \(3^{4x−2}\) \(= 3^4 = 81\)

Thus, in terms of \(m\), \(3^{4x−2}\) must be (C) \(9m^2\) , Answer must be (C)
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Re: If m=9^(x−1), then in terms of m, 3^(4x−2) &nbs [#permalink] 08 Jul 2018, 07:31
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