The constraint on the argument

Before manipulating any logarithm one must recall which numbers may appear as the argument.

Warning — Constraint on the argument

The argument of the logarithm must be strictly positive: $\log_a(y)$ is defined only for $y > 0$. This is because the image of the exponential is $(0;+\infty)$, so non-positive numbers cannot be the result of $a^x$. It is the most typical mistake in Year Three exercises: forgetting the existence condition (EC) $\text{argument}>0$.

Links

Topics: Logarithmic function
Concepts: Existence conditions · Logarithm
Functions: Logarithmic function