# LogLogplot of an equation

i need some help using LogLogPlot for graphing an equation that has various values of a parameter so that I get a set of curves on the plot. The equation is as follows:

(1/L^.5) + 2 Log10[(2.51/re L^.5)+.27/(d/k)]==0


re ranges from 4x10^3 to 10^7 and d/k takes on values of 50,200,1000,5000,100000.

So I should have 5 curves on my plot of Log10[L] vs Log10[re].

I'm not sure how to set this up in Mathematica.

• How far did you get? – Johu Jun 24 '16 at 7:35
• Are you sure the form is right? This equation has no solution. – Feyre Jun 24 '16 at 8:37
• @Feyre Solve doesn't have an issue with it. – rcollyer Jun 24 '16 at 13:16

In such cases, it is easier to do a variable transformation.

logplot[var1_, var2_, func_] := Module[{f, z1, z2, l11, l12, l21, l22},
f = func /. {var1 -> 10.^z1, var2 -> 10.^z2};
l11 = Log10[4 10^3]; l12 = Log10[10^7];
l21 = Log10[.1]; l22 = Log10[1];
ContourPlot[f, {z1, l11, l12}, {z2, l21, l22},
FrameTicks -> {Table[{x, 10^ToString[x]}, {x, 4, 7}],
Table[{x, 10^ToString[x]}, {x, -1, 0, .2}], None, None}]]

logplot[re, L, (1/L^.5) + 2 Log10[(2.51/re L^.5) + .27/(5000)]]


You can customise the FrameTicks or FrameLabel in logplot.