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Finding x with ln(a)/ln(b) as the answer. Help needed!

  1. Feb 22, 2009 #1
    1. The problem statement, all variables and given/known data
    http://img213.imageshack.us/img213/2327/nummer1.jpg [Broken]


    2. Relevant equations



    3. The attempt at a solution
    I find that that 3x*42x+1=4*48x
    and 6x+2=36x

    then i but ln(4*48x)=ln(48)*x+2*ln(2)
    and ln(36x)=2*ln(6)*x
    we get: ln(48)*x+2*ln(2)=2*ln(6)*x

    Now my proplem is; Is this all correct and what how do i move them around so i get x? I im really bad at moving those number around but x seems to dissapear for me!
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Feb 22, 2009 #2
    If you have trouble with this, simplify the equation in your head so that you have only x and constants which don't depend on x. In your case, ln(48)*x+2*ln(2)=2*ln(6)*x should look like Ax + B = Cx.
    From algebra, you can add the same number or variable to both sides and preserve the equality:
    Ax + B - Ax = Cx - Ax
    B = Cx - Ax
    When you are done, you can replace the dummies A, B and C with the real constants.
     
  4. Feb 22, 2009 #3
    then i get 2*ln(2)=2*ln(6)*x-ln(4)4*x
    2*ln(2)=2*ln(3)*x


    and then i move them again:
    (2*ln(2))/(2*ln(3))=(ln(2))/(ln(3))=x And that should be the answer!
    Thanks!
    My teacher is utterly baflet over my lack of abillity to grasp some of the simpler aspect while having no trubles with some of the more advancet aspects... But that dummy tecnique i am sure will help me out with these things in the future. Thanks a lot! :-)
     
  5. Feb 22, 2009 #4
    [itex] 6^{x+2} = 36^x [/itex]
    Let x = 3
    [itex] 6^5 = 7776 [/itex]
    [itex] 36^3 = 46,656 [/itex]

    [itex] 6^{x+2} = 36.6^x [/itex]
     
    Last edited by a moderator: May 4, 2017
  6. Apr 10, 2010 #5
    .........................................................................................
    . 6^(x+2)=36^x - false - {a^(x+y)=(a^y)^x} .
    . a^(x+y)=(a^x)*(a^y) - true
    . only a^(x*y)=(a^y)*x...then 6^(x+2)=(6^x)*(6^2)=36*(6^x)
    .........................................................................................
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    ..y
    ...
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    .....a
    ......z
    .......a
    ........K
    .........
    ..........R
    ...........O
     
  7. Apr 10, 2010 #6
    Yeah what I wrote is wrong but it was a long time ago.
     
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