Signal Integrity Issues and Printed Circuit Board Design

Appendix C. Logarithms

This appendix covers the definition of logarithms (logs), how we convert from logs of one base to logs of another base, and why we care about using logs in the first place.

Definition

A logarithm is an exponent of a number we call the base of the log. In general, if we have an expression of the form y = a^x, we say we take the log (to the base a) of y to obtain x, or log_a(y) = x. This looks kind of abstract, so lets look at the most common form of logarithm called, appropriately enough, a common log:

(We omit the subscript 10 in common logs, assuming it is understood.)

In this illustration, the base is 10 and the log is .5. Similarly, ...