Suppose, $p$ is a real negative number. However, $p^2$ is positive. Now,
$$\ln(p^2) = 2 \ln(p)\tag{1}$$
Question:
- Is $(1)$ valid to write?
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6$\begingroup$ Probably not valid in your context. If you start taking logs of negative numbers, you push yourself into complex numbers and then $\ln$ could have multiple values. You have to choose a "branch" of $\ln$ and then you still have to be careful. $\endgroup$– B. GoddardOct 12, 2021 at 11:26
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1 Answer
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No!
For exactly the reason you mention.
However, for $p\in\mathbb{R}$, $p\neq 0$, it is correct to write $\ln(p^2) = 2\ln(|p|)$.
