HSC Together Year 11 Maths Advanced: Logarithmic Laws

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Logarithmic Laws

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.

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