Mathematica Plotting Log as part of an equation in mathematica

AI Thread Summary
The discussion centers on plotting logarithmic equations in Mathematica, specifically the equation y = 25x / log10(x) - 50x. The user aims to manipulate variables to adjust the steepness of the curve, with the intention of modeling a water table influenced by rock porosity and well flow. The user references a specific formula for well discharge, Q = 2π K (Db - Dm) (Dw - Dm) / ln(Ri/Rw), emphasizing the relationship between well characteristics and the resulting graph. They seek to simplify this formula to replicate a specific graph depicting water table behavior, noting that the radius of influence of wells can vary based on their arrangement. The user also provides examples of how to plot both base 10 and natural logarithms in Mathematica, indicating a desire for further experimentation with different variables and parameters.
nimbus2506
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Hello I'm trying to plot log as part of an equation in mathematica and it does not seem to be working for me.

for example I'm using Plot y = 25x / log10 (x) - 50x

I'm just experimenting with different numbers and formulas to see what happens to the log curve.

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What I'm doing in more detail, is that I want to be able to change variables so that the curve can become steeper or shallower. I want to introduce about 4 or 5 different variables to control it.

http://en.wikipedia.org/wiki/File:WellHead.gif

I want to try and mimic and simplify this formula to produce the graph above. Where the water table level is controlled by the porosity of the rock and the flow of the well. Low porosity and low discharge from the well result in a steep curve and vise versa.

Q = 2π K (Db - Dm) (Dw - Dm) / ln (Ri/Rw)

where Q = safe well discharge - i.e. the steady state discharge at which no overdraught or groundwater depletion occurs - (m3/day), K = uniform hydraulic conductivity of the soil (m/day), D = depth below soil surface, Db = depth of the bottom of the well equal to the depth of the impermeable base (m), Dm = depth of the watertable midway between the wells (m), Dw is the depth of the water level inside the well (m), Ri = radius of influence of the well (m), Rw=radius of the well (m), ln = natural logarithm, and π = the number pi.

The radius of influence of the wells depends on the pattern of the well field, which may be triangular, square, or rectangular. It can be found as:

Ri = sqrt (At/πN)

http://en.wikipedia.org/wiki/Well_drainage
 
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For base 10 log

Plot[25x / Log[10,x] - 50x,{x,1,100}]

For natural log

Plot[2π K (Db - Dm) (Dw - Dm) / Log[Ri/Rw],{something,somethingelse,somethingother}]
 

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