# Trouble with using a log10 function in NonlinearModelFit

I was wondering why won't mathematica give a result where the function is also Log10, instead it gives the ordinary Log. Is it because the Log fits the problem better than the Log10 or... ?

Clear[x, a, b, c, d]

Data = {{0, 0}, {1, 6.91}, {2, 9.2}, {3, 11.4}, {4, 13.4}, {24,
39}, {25, 40.5}};

aa = NonlinearModelFit[Data, {a + b*Log10[c*x + d], c > 0, d > 0}, {a, b, c, d}, x];

aa // Normal

Show[Plot[aa[x], {x, 0, 100}, PlotRange -> All], ListPlot[Data, PlotStyle -> Directive[Red, PointSize[0.02]]]]

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Just type Log10[x] on a line and execute. What do you see? – Sjoerd C. de Vries Jun 6 '14 at 8:13
Please see: Display Log with desired notation in output – Mr.Wizard Jun 7 '14 at 14:51

Replace[Normal@aa, Log[val_] :> Defer[Log10[val^Log[10]]], Infinity]

I feel Log[val_] :> Log[10] Defer[Log10[val]] is more what is desired: $-75.4281+47.393 \log _{10}(9.28813 x+41.0739)$ rather than $-75.4281+20.5825 \log _{10}\left((9.28813 x+41.0739)^{\log 10}\right)$. – Rahul Jun 6 '14 at 8:12
@RahulNarain: You're probably right, since they're equivalent I suppose it depends where one wants the Log[10] to appear... – ciao Jun 6 '14 at 8:22