Math Help - Logarithm laws?

1. Logarithm laws?

Hi

$ln(x^{2})$ is defined for all $x \neq 0$

But, using basic logarithm law:

$ln(x^{2}) = 2 \cdot ln(x)$

???

2. Originally Posted by Twig
Hi

$ln(x^{2})$ is defined for all $x \neq 0$

But, using basic logarithm law:

$ln(x^{2}) = 2 \cdot ln(x)$

???
ln(x) is still undefined for x=0 so I'm not sure what you're trying to ask

3. Originally Posted by Twig
$ln(x^{2})$ is defined for all $x \neq 0$
But, using basic logarithm law:
$ln(x^{2}) = 2 \cdot ln(x)$
It works like this: $\sqrt {x^2 } = \left| x \right|$.
Thus, $\ln \left( {x^2 } \right) = 2\ln \left( {\left| x \right|} \right)$.

4. Let $f(x) = ln(x^{2})$

Then, $D_{f}=\mathbb{R}$ , except $x = 0$

But, by writing $2 \cdot ln(x)$ I dont have the same domain anymore. Now I need $x > 0$