The document discusses properties and theorems of logarithmic functions including: 1) Logarithmic functions can be combined using addition/subtraction when the bases are the same. 2) Logarithmic functions with composite bases can be rewritten as a single logarithm using laws such as (M·N) = logM + logN. 3) Examples show how to use logarithmic laws to evaluate expressions and combine or simplify logarithmic terms.