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# If 3^(7-n)=3^(n) -6(9^(1/2n-1)), what is the value of n+2?

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Joined: 05 Dec 2011
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If 3^(7-n)=3^(n) -6(9^(1/2n-1)), what is the value of n+2?  [#permalink]

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Updated on: 28 Dec 2016, 06:44
6
00:00

Difficulty:

55% (hard)

Question Stats:

73% (02:25) correct 27% (02:58) wrong based on 144 sessions

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If $$3^{(7-n)}=3^n -6(9^{(n/2-1)})$$, what is the value of n+2?

A. -3
B. 3
C. 4
D. 6
E. 13

Also what level would this be 600-700?

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Originally posted by geno5 on 14 Jun 2012, 17:56.
Last edited by Bunuel on 28 Dec 2016, 06:44, edited 4 times in total.
Moved to PS subforum.
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Re: If 3^(7-n)=3^(n) -6(9^(1/2n-1)), what is the value of n+2?  [#permalink]

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14 Jun 2012, 22:16
1
geno5 wrote:
If 3^(7-n)=3^(n) -6(9^(1/2n-1)), what is the value of n+2?

A)-3
B)3
C)4
D)6
E)13

Also what level would this be 600-700?

$$3^{7-n} = 3^n -6(9^{\frac{1}{2}n-1})$$

The first thing I can do is change 9 to 3 since that's a basic step in most exponent questions.

$$3^{7-n} = 3^n -6(3^{2*(\frac{1}{2}n-1)})$$
$$3^{7-n} = 3^n -6(3^{n-2})$$

Now, we know that 6 = 2*3 (I want to bring everything in terms of 3 to be able to simplify)
$$3^{7-n} = 3^n -2*3^{n-1}$$

All we can do when terms are added/subtracted is take something common. So we take $$3^{n-1}$$ common from the terms on the RHS.
$$3^{7-n} = 3^{n-1}(3 -2)$$
Now, we know what to do with this!
7-n = n - 1
n = 4

And yes, the question is 600 - 700 level.
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Re: If 3^(7-n)=3^(n) -6(9^(1/2n-1)), what is the value of n+2?  [#permalink]

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14 Jun 2012, 22:34
I understand how to get to 3^(7-n)=3^(n) - 2*3^(n-1).

But not how you got to the next stage of

3^(7-n)=3^(n-1)(3-2) I am mainly concerned with this 3^n where does it go or fit? How do you get (3-2)?

Sorry for not posting in math form.
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Re: If 3^(7-n)=3^(n) -6(9^(1/2n-1)), what is the value of n+2?  [#permalink]

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14 Jun 2012, 23:48
geno5 wrote:
I understand how to get to 3^(7-n)=3^(n) - 2*3^(n-1).

But not how you got to the next stage of

3^(7-n)=3^(n-1)(3-2) I am mainly concerned with this 3^n where does it go or fit? How do you get (3-2)?

Sorry for not posting in math form.

Say, you have 3^5 - 2*3^4 and you want to take something common out of them.

$$3^5 - 2*3^4$$
= $$3*3^4 - 2*3^4$$
= $$3^4 ( 3 - 2)$$

Similarly, if you have $$3^n - 2*3^{n-1}$$
= $$3*3^{n-1} - 2*3^{n-1}$$
= $$3^{n-1}(3 - 2)$$
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Re: If 3^(7-n)=3^(n) -6(9^(1/2n-1)), what is the value of n+2?  [#permalink]

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15 Jun 2012, 03:04
geno5 wrote:
If 3^(7-n)=3^(n) -6(9^(1/2n-1)), what is the value of n+2?

A. -3
B. 3
C. 4
D. 6
E. 13

Also what level would this be 600-700?

I'd agree with Karishma that it's ~650 level question.

For more on number theory and exponents check: math-number-theory-88376.html

DS questions on exponents: search.php?search_id=tag&tag_id=39
PS questions on exponents: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

Hope it helps.
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Re: If 3^(7-n)=3^(n) -6(9^(1/2n-1)), what is the value of n+2?  [#permalink]

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07 Apr 2014, 21:53
In the question asked, there is a bracket to the power of 9

$$9^{(\frac{1}{2}n-1)}$$

$$= 3^{2 * \frac{n-2}{2}}$$

$$= 3^{n-2}$$

Back to the equation

$$3^{7-n} = 3^n - 6 * 3^{n-2}$$

$$3^{7-n} = 3^n - 6 * \frac{3^n}{9}$$

$$3^{7-n} = 3^n - 2 * \frac{3^n}{3}$$

$$3^{7-n} = 3^n ( 1 - \frac{2}{3})$$

$$3^{7-n} = \frac{3^n}{3}$$

$$3^{7-n} = 3^{n-1}$$

7-n = n-1

2n = 8

n = 4

n+2 = 6

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Re: If 3^(7-n)=3^(n) -6(9^(1/2n-1)), what is the value of n+2?  [#permalink]

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07 Apr 2014, 22:33
PareshGmat wrote:
In the question asked, there is a bracket to the power of 9

$$9^{(\frac{1}{2}n-1)}$$

$$= 3^{2 * \frac{n-2}{2}}$$

$$= 3^{n-2}$$

Back to the equation

$$3^{7-n} = 3^n - 6 * 3^{n-2}$$

$$3^{7-n} = 3^n - 6 * \frac{3^n}{9}$$

$$3^{7-n} = 3^n - 2 * \frac{3^n}{3}$$

$$3^{7-n} = 3^n ( 1 - \frac{2}{3})$$

$$3^{7-n} = \frac{3^n}{3}$$

$$3^{7-n} = 3^{n-1}$$

7-n = n-1

2n = 8

n = 4

n+2 = 6

Yes, you get n as 4 and n+2 as 6 which is correct.
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Re: If 3^(7-n)=3^(n) -6(9^(1/2n-1)), what is the value of n+2?  [#permalink]

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