Factsheet: Laws of logarithms
The associated study guide for this factsheet is Guide: Introduction to logarithms. If you would like to know more about logarithms, please read the guide.
Throughout this factsheet, \(a,k, x,\) and \(y\) are positive real numbers, and \(n\) is a real number, with \(a, k \neq 1\).
Laws of logarithms
Law 1 - Product Rule: \[\log_a(x) + \log_a(y) = \log_a(xy)\]
Law 2 - Quotient Rule: \[\log_a(x) - \log_a(y) = \log_a(\frac{x}{y})\]
Law 3 - Power Rule: \[\log_a(x^n) = n\log_a(x)\]
Law 4 - Zero Rule: \[\log_a(1) = 0\]
Law 5 - Identity Rule: \[\log_a(a) = 1\]
Law 6 - Change of Base Rule: \[\log_a(x) = \frac{\log_k(x)}{\log_k(a)}\]
For more on the subject, please go to Guide: Introduction to logarithms
Version history
v1.0: created in 02/25 by Millie Pike as part of a University of St Andrews VIP project.