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If 3^(2n) = (1/9)^(n+2), what is the value of n?
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20 Feb 2021, 06:01
20 Feb 2021, 06:01
1
Expert Reply
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Question Stats:
69% (01:08) correct
30% (01:30) wrong based on 26 sessions
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If \(3^{(2n)} = (\frac{1}{9})^{(n+2)}\), what is the value of n?
A. -2
B. -1
C. 0
D. 1
E. 2
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. -2
B. -1
C. 0
D. 1
E. 2
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
If 3^(2n) = (1/9)^(n+2), what is the value of n?
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20 Feb 2021, 06:43
20 Feb 2021, 06:43
1
Solution:
\(3^2^n\)=\(\frac{1}{9}^n^+^2\)
\(\frac{1}{9}^n^+^2\)=\(3^-^2^(^n^+^2^)\)=\(3^-^2^n^-^4\)
\(3^2^n\)=\(3^-^2^n^-^4\)
2n=-2n-4
2n+2n=-4
4n=-4
n=-1
IMO B
Hope this helps!
\(3^2^n\)=\(\frac{1}{9}^n^+^2\)
\(\frac{1}{9}^n^+^2\)=\(3^-^2^(^n^+^2^)\)=\(3^-^2^n^-^4\)
\(3^2^n\)=\(3^-^2^n^-^4\)
2n=-2n-4
2n+2n=-4
4n=-4
n=-1
IMO B
Hope this helps!
Re: If 3^(2n) = (1/9)^(n+2), what is the value of n?
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20 Feb 2021, 06:56
20 Feb 2021, 06:56
1
On the left side we have a whole number: 3 and right side we have a fraction: 1/9. Both have some exponents. So, for positive answer choices, both sides will not be equal, hence eliminate C, D, E from the answer choices.
Now, We need to backsolve using either A or B. Putting the value of B (-1) we have got the value of both sides is equal.
Now, We need to backsolve using either A or B. Putting the value of B (-1) we have got the value of both sides is equal.
