Notation $\ln|x|$ vs. $\ln(x)$ Years ago, when I was taught about the function $\ln$ (logarithm in base $e$), all of my teachers and our book, too, insisted that we should write input of this function inside the absolute value notation and I am doing this since now. But, now when I am reading some university books or some answers on this site, I see in most answers, people write $\ln(x)$  using parentheses. It's been a question for a long time to me why people just use parentheses instead and how it is not wrong conventionally? I am sure if I used $\ln(x)$ in high school, it would've always been possible to get a minus point! I am a university student now. Can I write $\ln(x)$ safely and is it conventionally acceptable in mathematics? (I mean, in general, for $\ln(f(x))$ not only $\ln(x)$)

Your book is an outlier. $\ln(x)$ is different from $\ln|x|$; the latter is practically only encountered as the indefinite integral of $\frac1x$ from $0$ and is the result of precomposing the absolute value function to $\ln(x)$.
An increasing number of sources I read, and my own answers on this site, are lazy enough to go all the way and omit brackets: $\ln x$.
