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Rewrite a power

  1. Mar 27, 2009 #1
    1. The problem statement, all variables and given/known data
    Rewrite y = 5x in the form 3kx


    2. Relevant equations

    no idea

    3. The attempt at a solution

    I cant really attempt this because i dont have a clue where to start. Ive looked in all my maths books and it says nothing on how to do this. Our unit is partially based on inverses and differentation so im guessing its something to do with that.

    By guessing and typing random numbers into the calculator, i know that k is equal to 1.465

    example :

    52 = 25
    31.465 x 2 = 25

    thats all i can gather, but how do i show my working out/correct method? :(
     
  2. jcsd
  3. Mar 27, 2009 #2

    rock.freak667

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    Homework Helper

    well if you want 3^(kx)=5^x

    take logs to find k.
     
  4. Mar 28, 2009 #3
    how do i do that?
     
  5. Mar 28, 2009 #4
    Have you studied logarithms?
    If you have, use log a^b = b log a to find the value of k.
     
  6. Mar 28, 2009 #5

    lanedance

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    Homework Helper

    do you know about logarithmic functions?

    take the log of both sides and from the log laws, you can show log(y^k) = k.log(y)
     
  7. Mar 28, 2009 #6
    so u mean like...

    (let a = 5)
    (let b = 2)

    log 52 = 2 log 5
    = 1.39

    but, the value of k should be 1.465.


    what about...
    5x = 3kx
    0 = 5x - 3kx
    0 = 5 -3k
    3k = 5
    k = (log 5) divided by (log 3)

    therefore, k = 1.464973521

    so....5x = 31.465x
     
    Last edited: Mar 28, 2009
  8. Mar 29, 2009 #7

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    No, that does not follow. You cannot just "cancel" exponents like that.
    You can, directly from your original equation say that
    5x= 3kx= (3k)x and NOW take the "xth" root of both sides: 5= 3k.

    That works, with my correction to your reasoning. What people were suggesting you do is simpler: just take the logarithm of both sides of the original equation:
    log(5x)= log(3kx)
    x log(5)= kx log(3)
    Since this is to be true for all x, you can take x non-zero and divide both sides by x:
    log(5)= k log(3) so k= log(5)/log(3).
     
    Last edited: Mar 30, 2009
  9. Mar 30, 2009 #8
    ah i see, thanx for the help!
     
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