New posts in Logarithms

Question regarding a series that contains logarithms

The real function $f$ such that $\log \cdots \log (f)$ is strictly convex on its domain for any number of $\log$'s

Is there $k\in\mathbb{R}-\mathbb{Z}$ such that $2^k\in\mathbb{N}$ and $3^k\in\mathbb{N}?$

Why is $\frac{d}{dx}\ln |x|=\frac 1x$

Is $\ln (x/y) = \ln |x| - \ln |y|$?

Is there a reason why $\text{Arg}(z)$ behaves like a logarithm?

Restrictions on laws

Calculating $\int_0^1\frac{\ln^2x\ln(1-x)}{1-x}dx$ without using Beta function and Euler sum.

$0 \leq u - \ln(1+u) \leq u^2$ for $\mid u\mid < \frac{1}{2}$

Justifying $\sum_{n=0}^\infty\log(1+x^{2^n}) = -\log(1-x)$ for $0\le x<1$