LogGamma[z] gives the logarithm of the gamma function log \[CapitalGamma](z).
LogicalExpand[expr] expands out logical combinations of equations, inequalities, and other functions.
LogIntegral[z] is the logarithmic integral function li(z).
LogisticDistribution[\[Mu], \[Beta]] represents a logistic distribution with mean \[Mu] and scale parameter \[Beta].
LogitModelFit[{y_1, y_2, ...}, {f_1, f_2, ...}, x] constructs a binomial logistic regression model of the form 1/(1 + E -(\[Beta]_0 + \[Beta]_1 f_1 + \[Beta]_2 f_2 + \ ...)) ...
LogLikelihood[dist, {x_1, x_2, ...}] gives the log-likelihood function for observations x_1, x_2, ... from the distribution dist.
LogLinearPlot[f, {x, x_min, x_max}] generates a log-linear plot of f as a function of x from x_min to x_max. LogLinearPlot[{f_1, f_2, ...}, {x, x_min, x_max}] generates ...
LogLogisticDistribution[\[Gamma], \[Sigma]] represents a log-logistic distribution with shape parameter \[Gamma] and scale parameter \[Sigma].
LogLogPlot[f, {x, x_min, x_max}] generates a log-log plot of f as function of x from x_min to x_max. LogLogPlot[{f_1, f_2, ...}, {x, x_min, x_max}] generates log-log plots of ...
Log
(Built-in Mathematica Symbol) Log[z] gives the natural logarithm of z (logarithm to base e). Log[b, z] gives the logarithm to base b.