What are logarithmic laws?
In this post, we derive the logarithmic laws from the index laws and use the algebraic properties of logarithms to simplify and evaluate logarithmic expressions, as a part of the Prelim Maths Advanced course under the topic Exponential and Logarithmic Functions and sub-part Logarithmic Laws and Applications. The logarithmic laws are as follows:
- log_{a}m + log_{a}n = log_{a}(mn)
- log_{a}m - log_{a}n = log_{a}(\frac{m}{n})
- log_{a}(m^{n}) = n log_{a}m
- log_{a}a = 1
- log_{a}(1) = 0
- log_{a}(\frac{1}{x}) = -log_{a}x
The following three videos are an in-depth clear explanation of what logarithm laws are, giving examples to complement the explanations.
Part 1: Adding
Part 2: Subtracting
