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Natural logarithm equation

  1. Mar 4, 2013 #1
    Solve the following equation for x

    16-12ln(7x)=47

    I know I need to isolate x . however I am unsure how to get ln(7x) separated.

    what i have so far

    ln(7x)=-31/12
     
  2. jcsd
  3. Mar 4, 2013 #2

    SteamKing

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    e^(ln(y)) = y

    e = 2.71828...
     
  4. Mar 5, 2013 #3

    HallsofIvy

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    You always solve an equation for a variable such as x by doing the reverse of what has been done to it (to both sides, of course).

    If you were asked to evaluate 23- 9ln(4x) (I am using different numbers so you can apply the same idea to your problem) for a given value of x, you would:
    1) multiply by 4: 4x.
    2) take the natural logarithn: ln(4x)
    3) multiply by -9: -9 ln(7x)
    4) add 23: 23- 12 ln(7x)

    To solve for x, do the opposite: do the opposite of each step, in the opposite order. The opposite of "add 23" is "subtract 23", the opposite of "multiply by -9" is "divide by -9", the opposite of "multiply by 4" is "divide by 4", and the opposite of "take the natural logarithm" is "take the exponential".

    Starting from 23- 9 ln(4x)= 85:
    1) subtract 23: 23- 9ln(4x)- 23= 84- 23, -9ln(4x)= 61
    2) divide by -9: -9ln(4x)/(-9)= 61/(-9), ln(4x)= -61/9
    3) take the exponential: eln(4x)= e-61/9: 4x= e- 61/9[/tex]
    4) divide by 4: 4x/4= e-61/9/4, x= e-61/9/4.

    You will need to use a calculator to actually evaluate e-61/9.
     
    Last edited: Mar 5, 2013
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