If 3^m3^m3^m = 9^n, then m/n = : Problem Solving (PS)

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Bunuel

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If 3^m3^m3^m = 9^n, then m/n = [#permalink]

04 Nov 2014, 10:21

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If \(3^m3^m3^m = 9^n\), then \(\frac{m}{n} =\)

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3

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Re: If 3^m3^m3^m = 9^n, then m/n = [#permalink]

04 Nov 2014, 18:10

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3^m3^m3^m = 9^n
3^(m+m+m)=(3^2)^n
3^3m=3^2n
3m=2n
m/n = 2/3

Bunuel wrote:

Tough and Tricky questions: Exponents.

If 3^m3^m3^m = 9^n, then m/n =

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3

Kudos for a correct solution.

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Re: If 3^m3^m3^m = 9^n, then m/n = [#permalink]

04 Nov 2014, 23:23

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3^m*3^m*3^m= 9^n
3^(m+m+m)= 3^2n
3^3m=3^2n

=> 3m=2n => m/n=2/3

answer is b...

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Re: If 3^m3^m3^m = 9^n, then m/n = [#permalink]

12 Nov 2014, 19:12

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\(3^m 3^m 3^m = 9^n\)

\((3*3*3)^{m} = 3^{2n}\)

\(3^{3m} = 3^{2n}\)

Bases are same; equating powers

3m = 2n

\(\frac{m}{n} = \frac{2}{3}\)

Answer = B

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Re: If 3^m3^m3^m = 9^n, then m/n = [#permalink]

15 Feb 2015, 14:44

I also soved it, but a bit differently. Thank you for reminding me of this much easier and logical way!

What I did was to test powers of 3 that would lead to 9.

So, we have 3 raised to the same power 3 times and 9 raised to another power one time: 3^m3^m3^m = 9^n

What I did was test 3 raised to the power of 2 like this:
3^2*3^2*3^2 = 9*9*9 = 9^3. This means that m=2 and n=3. So, m/n=2/3.

It wouldn't be that hard ot back solve using the answer choices as well.

TeamGMATIFY

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Re: If 3^m3^m3^m = 9^n, then m/n = [#permalink]

23 Feb 2016, 02:53

Expert Reply

Bunuel wrote:

Tough and Tricky questions: Exponents.

If 3^m3^m3^m = 9^n, then m/n =

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3

Kudos for a correct solution.

The easiest way to solve such questions is to bring the numbers in the same base.
Always try to bring the base to the lowest number possible, in this case: 3

3^m*3^m*3^m = 9^n
3^(3m) = 3^2n
Since the bases are same, we can equate the powers.

3m = 2n
Therefore m/n = 2/3
Option B

GMATasian

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Joined: 07 Dec 2017

Posts: 1

Re: If 3^m3^m3^m = 9^n, then m/n = [#permalink]

23 Feb 2018, 00:21

TeamGMATIFY wrote:

Bunuel wrote:

Tough and Tricky questions: Exponents.

If 3^m3^m3^m = 9^n, then m/n =

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3

Kudos for a correct solution.

The easiest way to solve such questions is to bring the numbers in the same base.
Always try to bring the base to the lowest number possible, in this case: 3

3^m*3^m*3^m = 9^n
3^(3m) = 3^2n
Since the bases are same, we can equate the powers.

3m = 2n
Therefore m/n = 2/3
Option B

---

Hi sorry for a stupid question. The question asked for m/n right?

why is the answer 2/3 and NOT 3/2? the answer we got is 2m=2n

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Bunuel

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Posts: 92747

Re: If 3^m3^m3^m = 9^n, then m/n = [#permalink]

23 Feb 2018, 00:34

2

Kudos

Expert Reply

GMATasian wrote:

TeamGMATIFY wrote:

Bunuel wrote:

Tough and Tricky questions: Exponents.

If 3^m3^m3^m = 9^n, then m/n =

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3

Kudos for a correct solution.

The easiest way to solve such questions is to bring the numbers in the same base.
Always try to bring the base to the lowest number possible, in this case: 3

3^m*3^m*3^m = 9^n
3^(3m) = 3^2n
Since the bases are same, we can equate the powers.

3m = 2n
Therefore m/n = 2/3
Option B

---

Hi sorry for a stupid question. The question asked for m/n right?

why is the answer 2/3 and NOT 3/2? the answer we got is 2m=2n

If \(3^m3^m3^m = 9^n\), then \(\frac{m}{n} =\)

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3

\(3^m3^m3^m = 9^n\);

\(3^{(m+m+m)} = 3^{2n}\)

\(3^{3m} = 3^{2n}\)

\(3m = 2n\);

Divide by n: \(3*\frac{m}{n}=2\).

Divide by 3: \(\frac{m}{n}=\frac{2}{3}\).

Answer: B.
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Re: If 3^m3^m3^m = 9^n, then m/n = [#permalink]

21 Mar 2018, 03:04

Bunuel wrote:

Tough and Tricky questions: Exponents.

If \(3^m3^m3^m = 9^n\), then \(\frac{m}{n} =\)

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3

Kudos for a correct solution.

\(3^m3^m3^m = 9^n\)

\(3^3m = 3^2n\)

As bases are same , we can equate powers,

\(3m = 2n\)

\(\frac{m}{n}= \frac{2}{3}\)

(B)
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hoang221

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Re: If 3^m3^m3^m = 9^n, then m/n = [#permalink]

21 Mar 2018, 03:18

Bunuel wrote:

Tough and Tricky questions: Exponents.

If \(3^m3^m3^m = 9^n\), then \(\frac{m}{n} =\)

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3

Kudos for a correct solution.

\(3^m3^m3^m = 9^n => 3^{3m} = 3^{2n} => 3m = 2n => \frac{m}{n} = \frac{2}{3}\) => (B)

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JeffTargetTestPrep

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Re: If 3^m3^m3^m = 9^n, then m/n = [#permalink]

22 Mar 2018, 15:45

Expert Reply

Bunuel wrote:

Tough and Tricky questions: Exponents.

If \(3^m3^m3^m = 9^n\), then \(\frac{m}{n} =\)

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3

When bases are the same, we add the exponents. Thus, 3^m*3^m*3^m = 3^3m. Simplifying the equation, we have:

3^3m = 9^n

3^3m = 3^2n

3m = 2n

m/n = 2/3

Answer: B
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EgmatQuantExpert

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Re: If 3^m3^m3^m = 9^n, then m/n = [#permalink]

26 Mar 2018, 11:08

Expert Reply

Solution:

Given:

• 3^m* 3^m * 3^m = 9^n
Working out:

We need to find the value of \(m/n\)

Per our conceptual knowledge, we know that if the numbers are in multiplicative form. We can add their powers, provided their bases are same.

Here, applying the same concept, we get:

Since the bases are same, we can equate the exponents.

Following the above process, we get:

Answer: Option B
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