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Power of n

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    How would u solve:
    3X27^1/2= 3^n
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    (Original post by Sophhhowa)
    How would u solve:
    3X27^1/2= 3^n
    Is that  3 \times 27^{\frac{1}{2}} = 3^n?
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    (Original post by SeanFM)
    Is that  3 \times 27^{\frac{1}{2}} = 3^n?
    Yeah
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    (Original post by Sophhhowa)
    Yeah
    What have you tried?

    Hint:
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    If everything on the left is a power of 3 then it is fairly easy to work out what n is)
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    (Original post by SeanFM)
    What have you tried?

    Hint:
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    If everything on the left is a power of 3 then it is fairly easy to work out what n is)
    Why is it a power of 3?
    Sorry I've never actually been taught how to do this so I'm completely lost
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    (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  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  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?
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    (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!

    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!

    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
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    (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?
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    (Original post by Sophhhowa)
    Actually is it 3^3?
    So 3^1X3^3= 3^4
    So n is 4?
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    (Original post by Sophhhowa)
    So 3^1X3^3= 3^4
    So n is 4?
    Very very close 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
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    3 \times 27^{\frac{1}{2}} = 3^n

3 \times (3^3)^{\frac{1}{2}} = 3^n

3 \times 3^{\frac{3}{2}} = 3^n

    Should be able to solve from there!
 
 
 
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