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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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geno5
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If 3^(7-n)=3^(n) -6(9^(1/2n-1)), what is the value of n+2? [#permalink] New post   Updated on: 28 Dec 2016, 06:44
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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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D

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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KarishmaB
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Re: If 3^(7-n)=3^(n) -6(9^(1/2n-1)), what is the value of n+2? [#permalink] New post   14 Jun 2012, 22:16
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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

Show Spoiler
D


Also what level would this be 600-700?


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

Adding and subtracting terms with exponents is tricky business.
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] New post   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] New post   14 Jun 2012, 23:48
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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] New post   15 Jun 2012, 03:04
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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] New post   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

Answer = D
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Re: If 3^(7-n)=3^(n) -6(9^(1/2n-1)), what is the value of n+2? [#permalink] New post   07 Apr 2014, 22:33
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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

Answer = D


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] New post   16 Aug 2022, 08:51
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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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