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How to make γ the subject of the formula? (logarithms involved)

  1. Nov 9, 2012 #1
    How to make γ the subject of the formula??? (logarithms involved)

    1. The problem statement, all variables and given/known data

    My problem here is that i want to make γ the subject of the formula so that i can calculate it since all other variables are know. As you can see from the equation below there are two γ inside the equation one on the left hand side and one on the right hand side of the equation which is inside the logarithm [log((qnet+γ)/pa)].

    The variables involved are shown below, however you do not really need to know what each one means since the problem here is about mathematics and how to make γ subject of the formula if thats possible but i did include all variables to make it easier to understand the equation

    γ = unit weight of soil = unknown
    γW = unit weight of water = 9.81
    Rf = friction ratio 0.5
    qnet = net cone resistance = 5.53
    pa = atmospheric pressure = 0.1


    2. Relevant equations

    Equation:


    γ/γW = 0.27 [log Rf] + 0.36 [log((qnet+γ)/pa)] +1.236


    3. The attempt at a solution

    γ/γW = 0.27 [log Rf] + 0.36 [log((qnet+γ)/pa)] +1.236

    Substituting Rf = friction ratio 0.5

    γ/γW = 0.27 [log 0.5] + 0.36 [log((qnet+γ)/pa)] +1.236

    γ/γW = -0.08 + 0.36 [log((qnet+γ)/pa)] +1.236

    γ/γW = -0.08 +1.236 + 0.36 [log((qnet+γ)/pa)]

    γ/γW = 1.15 + 0.36 [log((qnet+γ)/pa)]

    γ/γW - 1.15 = + 0.36 [log((qnet+γ)/pa)]

    (γ/γW - 1.15)/0.36 = log((qnet+γ)/pa)

    10(γ/γW - 1.15)/0.36 = (qnet+γ)/pa

    I am not sure what to do next, i dont know how to get both γ together. Some help would be really appreciated.

    Thank you.
     
  2. jcsd
  3. Nov 9, 2012 #2

    haruspex

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    Re: How to make γ the subject of the formula??? (logarithms involved)

    There is no closed form for mixes of functions like this. You will have to use approximation methods, iterative usually.
     
  4. Nov 9, 2012 #3
    Re: How to make γ the subject of the formula??? (logarithms involved)

    Ok thanks a lot for you reply
     
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