This document discusses properties of logarithms, including: 1) Logarithms with the same base "undo" each other according to the inverse function relationship between logarithms and exponents. 2) Logarithmic expressions can be expanded using properties to write them as sums or differences of individual logarithmic terms, or condensed into a single logarithm. 3) The change of base formula allows converting between logarithms with different bases, with common uses being to change to base 10 or the base of natural logarithms.