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

Question

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?

KarishmaB · Answer

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.

geno5 · Answer

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.

KarishmaB · Answer

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)

Bunuel · Answer

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.

PareshGmat · Answer

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

KarishmaB · Answer

Yes, you get n as 4 and n+2 as 6 which is correct.

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

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