Laws and Properties of Logarithms

Logarithms are not arbitrary rules — they are a direct consequence of the way exponents work. Every law of logarithms mirrors a corresponding law of exponents, so understanding one gives you the other for free. Once you see that $\log_b(mn) = \log_b m + \log_b n$ is just another way of saying $b^p \cdot b^q = b^{p+q}$, the properties stop being a list to memorise and become a natural toolkit for simplifying expressions. This section builds that conn …