Question Number 195647 by mathlove last updated on 06/Aug/23
$${f}\left({x}\right)=\frac{\mathrm{1276}}{\left({x}−\mathrm{1}\right)^{{ln}\frac{\mathrm{2}}{\mathrm{4589}}} } \\ $$$${domain}\:{f}\left({x}\right)=? \\ $$
Answered by Tokugami last updated on 17/Sep/23
$$\frac{\mathrm{1276}}{\left({x}−\mathrm{1}\right)^{\mathrm{ln}\left(\mathrm{2}\right)−\mathrm{ln}\left(\mathrm{4589}\right)} }=\mathrm{1276}\left({x}−\mathrm{1}\right)^{\mathrm{ln}\left(\mathrm{4589}\right)−\mathrm{ln}\left(\mathrm{2}\right)} \\ $$$$\mathrm{ln}\left(\frac{\mathrm{4589}}{\mathrm{2}}\right)\notin\mathbb{Z}\rightarrow\:{x}−\mathrm{1}\geqslant\mathrm{0} \\ $$$${x}\geqslant\mathrm{1} \\ $$