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Power of n

How would u solve:
3X27^1/2= 3^n
Original post by Sophhhowa
How would u solve:
3X27^1/2= 3^n


Is that 3×2712=3n 3 \times 27^{\frac{1}{2}} = 3^n?
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Sophhhowa
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Original post by SeanFM
Is that 3×2712=3n 3 \times 27^{\frac{1}{2}} = 3^n?


Yeah
Original post by Sophhhowa
Yeah


What have you tried? :h:

Hint:

Spoiler

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Original post by SeanFM
What have you tried? :h:

Hint:

Spoiler



Why is it a power of 3?
Sorry I've never actually been taught how to do this so I'm completely lost
Original post by Sophhhowa
Why is it a power of 3?
Sorry I've never actually been taught how to do this so I'm completely lost


If you had for example 2a×2b=25 2^a \times 2^b = 2^5 you would know that by law of indices a + b = 5.

Can you apply a similar logic here to find n?
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Original post by SeanFM
If you had for example 2a×2b=25 2^a \times 2^b = 2^5 you would know that by law of indices a + b = 5.

Can you apply a similar logic here to find n?


Yh I get that but surely to be able to add the indices the 3 and 27 would have to be the same number? How do I do that?
Original post by Sophhhowa
Yh I get that but surely to be able to add the indices the 3 and 27 would have to be the same number? How do I do that?


Exactly right! That is the first step of the problem! :smile:

If I asked you to write 27 as a power of 3, what would you say?

If you know the answer to that, then how about 27^(1/2)?
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Original post by SeanFM
Exactly right! That is the first step of the problem! :smile:

If I asked you to write 27 as a power of 3, what would you say?

If you know the answer to that, then how about 27^(1/2)?


Sorry I have no clue how to do that
Original post by Sophhhowa
Sorry I have no clue how to do that


No worries, if I say that 27 = 3 * 9... can you break that down further so that you can write 27 as 3^(...)?
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Original post by Sophhhowa
Sorry I have no clue how to do that


Actually is it 3^3?
Reply 11
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Original post by Sophhhowa
Actually is it 3^3?


So 3^1X3^3= 3^4
So n is 4?
Original post by Sophhhowa
So 3^1X3^3= 3^4
So n is 4?


Very very close :h: remember that it's 3*27^(1/2) though, not 3*27.
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Original post by Sophhhowa
So 3^1X3^3= 3^4
So n is 4?


No n is 2.5 coz it's 3^2/3
3×2712=3n[br]3×(33)12=3n[br]3×332=3n3 \times 27^{\frac{1}{2}} = 3^n[br]3 \times (3^3)^{\frac{1}{2}} = 3^n[br]3 \times 3^{\frac{3}{2}} = 3^n

Should be able to solve from there!

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