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We derive an analytic expression for the transitional column density value($s_t$) between the lognormal and power-law form of the probabilitydistribution function (PDF) in star-forming molecular clouds. Our expressionfor $s_t$ depends on the mean column density, the variance of the lognormalportion of the PDF, and the slope of the power-law portion of the PDF. We showthat $s_t$ can be related to physical quantities such as the sonic Mach numberof the flow and the power-law index for a self-gravitating isothermal sphere.This implies that the transition point between the lognormal and power-lawdensity/column density PDF represents the critical density where turbulent andthermal pressure balance, the so-called "post-shock density." We test ouranalytic prediction for the transition column density using dust PDFobservations reported in the literature as well as numerical MHD simulations ofself-gravitating supersonic turbulence with the Enzo code. We find excellentagreement between the analytic $s_t$ and the measured values from the numericalsimulations and observations (to within 1.5 A$_V$). We discuss the utility ofour expression for determining the properties of the PDF from unresolved lowdensity material in dust observations, for estimating the post-shock density,and for determining the HI-H$_2$ transition in clouds.

The Razor's Edge of Collapse: The Transition Point from Lognormal to Powerlaw in Molecular Cloud PDFs