Understandind M and N

[jg_macarthy]

Can anyone please shed light to why the answer to the below question is B and not D. When the problem gets to 3m=2n are they dividing both sides by 2n. making it 3m/2n = 2n/2n or 3m/2n = 1. Then multiplying each side by 2/3 to get m/n=2/3? Any help would be appreciated.


If m and n are non-zero numbers and 3m3m3m = 9n, then m/n =


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


In problems that involve exponential expressions on both sides of the equation, it is imperative to rewrite the bases so that either the same base or the same exponent appears on both sides of the equation. Here, we can get a common base by replacing the 9 with 32.

3m3m3m = 9n
3m3m3m = (32)n
33m = 32n

Since the bases are the same, the exponents must be equal.

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

The correct answer is B.

[jnelson0612]

jg, what you have posted is perfectly good. To get there just a little more quickly, I'd probably do the following steps:

I have 3m=2n and I want m/n. Let me start working to get that:

1) divide both sides by n. I then have 3m/n = 2

2) divide both sides by 3. I then have m/n = 2/3. Done!

[krishnan.anju1987]

It would be great if exponential signs were used in this question so that it would be easier for everyone to follow.

The correct question is
If 3^m) (3^m) (3^m) = 9^n, then m/n =
A)1/3
B)2/3
C)1
D)3/2
E)3

[RonPurewal]

It would be great if exponential signs were used in this question so that it would be easier for everyone to follow.

The correct question is
If 3^m) (3^m) (3^m) = 9^n, then m/n =
A)1/3
B)2/3
C)1
D)3/2
E)3

thanks for posting the actual question.