Question Number 163986 by mathlove last updated on 12/Jan/22
$$\sqrt[{\mathrm{3}}]{\mathrm{1000}}{ln}^{\mathrm{80}} \left({ln}\frac{\mathrm{8}}{\mathrm{5}}−{ln}\frac{\mathrm{8}{e}}{\mathrm{5}}\right)^{\mathrm{80}} \\ $$$${is}\:\:\:\:{simplified}\:\:{form}\:\:{equl}\:\:{to}=? \\ $$$$ \\ $$
Answered by nikif99 last updated on 12/Jan/22
$$\sqrt[{\mathrm{3}}]{\mathrm{1000}\:}\mathrm{ln}\:^{\mathrm{80}} \left(\mathrm{ln}\:\frac{\mathrm{8}}{\mathrm{5}}−\mathrm{ln}\:\frac{\mathrm{8}{e}}{\mathrm{5}}\right)^{\mathrm{80}} = \\ $$$$\mathrm{10}\:\mathrm{ln}\:^{\mathrm{80}} \:\left(\mathrm{ln}\:\frac{\mathrm{8}/\mathrm{5}}{\mathrm{8}{e}/\mathrm{5}}\right)^{\mathrm{80}} =\mathrm{10}\:\mathrm{ln}\:^{\mathrm{80}} \left(\mathrm{ln}\:\frac{\mathrm{1}}{{e}}\right)^{\mathrm{80}} = \\ $$$$\mathrm{10}\:\mathrm{ln}\:^{\mathrm{80}} \left(\mathrm{ln}\:\mathrm{1}−\mathrm{ln}\:{e}\right)^{\mathrm{80}} =\mathrm{10}\:\mathrm{ln}\:^{\mathrm{80}} \left(−\mathrm{1}\right)^{\mathrm{80}} = \\ $$$$\mathrm{10}\:\mathrm{ln}\:^{\mathrm{80}} \mathrm{1}=\mathrm{10}×\mathrm{0}^{\mathrm{80}} =\mathrm{0} \\ $$
Commented by mathlove last updated on 12/Jan/22
$${thanks} \\ $$