  The RG equation for the effective potential in the leading log (LL)
approximation is constructed which is valid for an arbitrary scalar field
theory in 4 dimensions. The solution to this equation sums up the leading
$\log\phi$ contributions to all orders of perturbation theory. In general, this
is the second order nonlinear partial differential equation, but in some cases
it can be reduced to the ordinary one. For particular examples, this equation
is solved numerically and the LL effective potential is constructed. The
solution has a characteristic discontinuity replacing the Landau pole typical
for the $\phi^4$ theory. For a power-like potential no new minima appear due to
the Coleman-Weinberg mechanism.
