If you are still interested in an answer to your question:
(mu)^= 1/n * sum_{i=1}^{n} Log10[x_i]
and
(sigma^2)^ = Ln[10]/n * sum_{i=1}^{n} (Log10[x_i]-(mu)^)^2
are maximum likelihood estimates for the parameters of your distribution with density function
f(x)=1/(Sqrt[2*Pi*Ln[10]]*Sigma*x)*10^(-(Log10[x]-mu)^2/(2*sigma^2))
Note the normalization by a factor of Sqrt[Ln[10]] to make
integral_{x=0}^{x=Inf} f(x) dx = 1.
Best wishes
Torsten.
