Quadratic irrationality exponents of certain numbers

The paper presents upper estimates for the non-quadraticity measure of the numbers $\sqrt{2k+1}\ln\bigr((k+1-\sqrt{2k+1})/k\bigl)$ and $\sqrt{2k-1}\operatorname{arctg}\bigr(\sqrt{2k-1}/(k-1)\bigl)$, where $k\in\mathbb{N}$. In particular, we improved an upper estimate for the non-quadraticity measure of $\ln2$.