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

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Senior Manager
Joined: 21 Oct 2013
Posts: 419
If m=9^(x−1), then in terms of m, 3^(4x−2)  [#permalink]

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03 Jun 2014, 13:20
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Difficulty:

55% (hard)

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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Joined: 02 Sep 2009
Posts: 51215
Re: If m=9^(x−1), then in terms of m, 3^(4x−2)  [#permalink]

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03 Jun 2014, 13:38
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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

$$3^{(4x-2)}=3^{2(2x-1)}=9^{(2x-1)}=9*9^{(2x-2)}=9*(9^{(x-1)})^2=9m^2$$.

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

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03 Jun 2014, 19:44
4
$$m = 9^{x-1}$$

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

$$m = 3^{2x - 2}$$

$$9m = 3^{2x}$$

Squaring both sides

$$81m^2 = 3^{4x}$$

Dividing both sides by 9

$$9m^2 = 3^{4x-2}$$

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

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

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