Lognormal distribution describes a large number of growth processes (e.g. expansion of population, cities, firms and industries, spreading of communicable epidemics,). The curve of Shannon entropy of lognormal distribution as function of the standard deviation is found to have a minimal slope. It is argued that assuming minimal slope leads to scaling relations that exhibits some geometrical similarity to the minimal surface energy principle. Precisely, the minimal slope occurs when the standard deviation parameters takes the value of 1/√6 and the maximal value of the distribution occurs at √e where e≃2.718 is the base of natural logarithm. It is surprising that these constants are very close to some observations in natural processes described by lognormal distribution.