The non-properties to avoid

The properties hold only for products and quotients: applying them to sums is the most widespread mistake.

Warning — Frequent non-properties

$\log(x+y) \ne \log x + \log y$. The logarithm is not additive over sums: it is only over products. This mistake is the most widespread and must be avoided at all costs.

Similarly $(\log x)^k \ne k\log x$ in general: the power property concerns the case in which the exponent is inside the argument, not outside.

Links

Topics: Logarithmic function
Concepts: Logarithm · Properties of logarithms
Functions: Logarithmic function