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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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07 Sep 2017, 23:23
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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. $$14$$

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

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Updated on: 08 Sep 2017, 01:09
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. $$14$$

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

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

(D)

Originally posted by sarathgopinath on 08 Sep 2017, 01:02.
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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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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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.

=> $$m = 3^{2x} * 2^{2x} / 3^x$$

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

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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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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. $$14$$

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

$$m = \frac{6^{2x}}{3^x}$$

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

$$m = \frac{2^{2x}*3^{2x}}{3^x}$$

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

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

$$m = 3^x2^{2x}$$

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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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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

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

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