The following elementary properties of logarithms to any base will be assumed to be familiar, and so they will not be discussed.

Basic properties of the logarithmic function

For any base a/0 such that a"/1, and any two real numbers x/0, y/0, we have:

1 loga a/1;

2 loga (xy )/loga x/loga y ;

3 loga [x /y ]/loga x/loga y ;

4 loga (x y )/y loga x ;

5 loga x/ln x /ln a ;

6 loga x/logb x /logb a for any b/0 such that b"/1.