useful mathematical facts in this appendix we give several useful mathematical facts we begin with some combinatorial definitions and facts logarithms and exponents the logarithm function is defined as log if bc the following identities hold for logarithms and exponents log ac log log log / log log log ac clog log (log )/log blog alog (ba) bac babc ba+ ba/bc ba- in additionwe have the followingproposition if and bthen loga logb < logc