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

[Kelles]

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

Homework Statement

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 that's 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

Homework Equations

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

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 don't know how to get both γ together. Some help would be really appreciated.

Thank you.

 

[haruspex]

There is no closed form for mixes of functions like this. You will have to use approximation methods, iterative usually.

 

[Kelles]

Ok thanks a lot for you reply