Question Number 110460 by ZiYangLee last updated on 29/Aug/20
$$\mathrm{Find}\:\mathrm{all}\:\mathrm{continuous}\:\mathrm{real}\:\mathrm{function}\:{f}\: \\ $$$$\mathrm{such}\:\mathrm{that}\: \\ $$$${f}\left(\mathrm{ln}\left({x}+{y}\right)\right)={f}\left(\mathrm{sin}\left({xy}\right)\right)+{f}\left(\mathrm{cos}\left({y}/{x}\right)\right) \\ $$$$\mathrm{for}\:\mathrm{all}\:{x},{y}\in\mathbb{R}^{+} . \\ $$