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f-x-1276-x-1-ln-2-4589-domain-f-x-




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

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