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If 3^x = 6^2x*1/m, which of the following is equivalent to m?

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If 3^x = 6^2x*1/m, which of the following is equivalent to m? [#permalink]

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New post 07 Sep 2017, 23:23
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

88% (00:54) correct 12% (01:17) wrong based on 52 sessions

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If 3^x = 6^2x*1/m, which of the following is equivalent to m? [#permalink]

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New post 08 Sep 2017, 01:02
Bunuel wrote:
If \(3^x = 6^{2x}*\frac{1}{m}\), which of the following is equivalent to m?


A. \(\frac{1}{4}\)

B. \(2^x\)

C. \(6^x\)

D. \(3^x2^{2x}\)

E. \(14\)


\(3^x = 6^{2x}*\frac{1}{m}\)
\({3^{x}} * m = (3*2)^{2x}\)
\({3^{x}} *m = 3^{2x}\)*\(2^{2x}\)

Now comparing both the sides, m should be equal to \(3^{x}*2^{2x}\)

(D)

Last edited by sarathgopinath on 08 Sep 2017, 01:09, edited 1 time in total.

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If 3^x = 6^2x*1/m, which of the following is equivalent to m? [#permalink]

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New post 08 Sep 2017, 01:08
Given: \(3^x = 6^{2x}*\frac{1}{m}\)

Since, we have been asked to find the value of m, we can re-write the equation as \(m = \frac{6^{2x}}{3^x}\)

Rules:

\(a^m = b^m*c^m\) (when \(a=b*c\))
\(\frac{a^{m}}{a^{n}} = a^{m-n}\)


Therefore, m can be simplified further as follows:

\(m = \frac{3^{2x}*2^{2x}}{3^x} = (2^{2x})*\frac{3^{2x}}{3^x} = 2^{2x}*3^{2x-x} = 3^x*2^{2x}\)(Option D)
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If 3^x = 6^2x*1/m, which of the following is equivalent to m? [#permalink]

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New post 08 Sep 2017, 05:26
\(3^x = 6^{2x} * 1/m => m= 6^{2x} / 3^x\) ; m is a non-zero number since it is already in denominator.

=> \(m = 3^{2x} * 2^{2x} / 3^x\)

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

Answer - D

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Re: If 3^x = 6^2x*1/m, which of the following is equivalent to m? [#permalink]

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New post 08 Sep 2017, 08:09
Bunuel wrote:
If \(3^x = 6^{2x}*\frac{1}{m}\), which of the following is equivalent to m?


A. \(\frac{1}{4}\)

B. \(2^x\)

C. \(6^x\)

D. \(3^x2^{2x}\)

E. \(14\)

\(3^x = 6^{2x}*\frac{1}{m}\)

\(m = \frac{6^{2x}}{3^x}\)

\(m = \frac{(2*3)^{2x}}{3^x}\)

\(m = \frac{2^{2x}*3^{2x}}{3^x}\)

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

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

\(m = 3^x2^{2x}\)

Answer (D)...

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Re: If 3^x = 6^2x*1/m, which of the following is equivalent to m? [#permalink]

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New post 11 Sep 2017, 15:57
Bunuel wrote:
If \(3^x = 6^{2x}*\frac{1}{m}\), which of the following is equivalent to m?


A. \(\frac{1}{4}\)

B. \(2^x\)

C. \(6^x\)

D. \(3^x2^{2x}\)

E. \(14\)


We can simplify the equation by first re-expressing 6^2x as (2 * 3)^2x = 2^2x * 3^2x:

3^x = 6^2x * 1/m

m = 6^2x/3^x

m = 2^2x * 3^2x/3^x

m = 2^2x * 3^x

Answer: D
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Re: If 3^x = 6^2x*1/m, which of the following is equivalent to m?   [#permalink] 11 Sep 2017, 15:57
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