Test

[Gerson W. Barbosa]

\[\ln\left({\frac{16\ln\left({x}\right)}{\ln\left({16\ln\left({x}\right)}\right)}}​\right)\]
where

\[x=878-\frac{1}{878^2-\frac{25}{21-\left({\frac{1}{40-\frac{1}{90}}}\right)^2}\sqrt{878^3}}\]


3.141592653589793238462(537)
(29 Apr 2024)

\[\left\{{\left[{2-\frac{1}{2^{19}-\left({58-\frac{1}{116+\phi^2}}\right)^2}}\right]\times\frac{9-100\sqrt{2}}{8+100\sqrt{2}}}\right\}^2\]
3.1415926535897932(632)
(24 Mar 2024)

\[\frac{10000\ln\left({5+\frac{1}{50000000}}\right)}{5123\left[{1+\left({\frac{7}{40000000}}\right)^2}\right]}\]
3.1415926535897932(413)
(14 Mar 2024)

\[\left({\frac{4+\frac{\phi+2}{200}}{3+\frac{\phi+2}{200}}}\right)^4\]
3.1415926(397)
(14 Mar 2024)

\[\frac{4\left({2500\ln\left({5}\right)+\frac{1}{99999+\sqrt{5}}}\right)}{5123}\]

\[\frac{10000\ln\left({5+\frac{1}{50000000}}\right)}{5123}\]

\(\sqrt[4]{\frac{2143+\left({6+\sqrt{6-\left({6^5-5}\right)^{-1}}}\right)^{-6}}{22}}\)

\(\frac{2^8-\frac{790}{516}}{3^4}\)


\(\frac{63}{25}\left({\frac{17+3x\sqrt{x}}{7+3x\sqrt{x}}}\right)\)

where

\(x=5+\frac{7}{5000000000+1000000\sqrt{5}}\)

or

\(x=5+\frac{7}{5000000000+\left({1000000+\sqrt{1000\times5!-e^5}}\right)\sqrt{5}}\)

Based on an approximation by Ramanujan ( x = 5 )


\(\frac{\ln\left({\frac{16\times\ln\left({878}\right)}{\ln\left({16\ln\left({878​}\right)}\right)}}\right)}{1+\left({\frac{5}{94+\sqrt{2}}}\right)^8}\)


\(\sqrt[4]{\frac{2143+\frac{1}{\left({6+\sqrt{6-\frac{1}{6^5-5}}}\right)^6}}{22}}\)


\(\sqrt[4]{\frac{2143}{22}+\frac{1}{32\left({500+\frac{1}{\sqrt{32-\frac{\sqrt{2}}{15}}}}\right)^2}}\)


\(e^{\sqrt[11_{3}]{\frac{2222_{4}-\frac{1}{22_{9}^{2}+22_{16}^{2}+\frac{1}{1111_{7}}}}{99_{10}}}}\)

https://latexeditor.lagrida.com/

\(\sqrt{\frac{878}{89-\frac{1}{\sqrt{625-\frac{33}{1385+\sqrt{\frac{2}{3}}}}}}}\)

\(e^{\pi}-\pi+\frac{1}{\left({\frac{10^5-1+\sqrt{2}}{10^4}+\frac{\pi\sqrt{2}}{4}}\right)\left({\frac{10^5-1+\sqrt{2}}{10^4}}\right)^2} \)

\(e^{\pi}-\pi-\frac{e}{\left({e^{-\pi^2}-\pi}\right)\pi^6}\)

\(\sqrt[4]{\frac{2143}{22}+\frac{1}{\left({2000\sqrt{2}+3}\right)^2-\frac{31999\sqrt{2}}{4}}}\)


\(\sqrt[4]{\frac{2143+\frac{1}{\left({6+\sqrt{6-\frac{1}{6^5-5}}}\right)^6}}{22}}\)




\(\frac{\ln\left({\frac{16\times\ln\left({878}\right)}{\ln\left({16\ln\left({878​}\right)}\right)}}\right)}{1+\left({\frac{5}{94+\sqrt{2}}}\right)^8}\)



\(\sqrt[4]{\frac{2143+\left({6-6^{-6}+\sqrt{6-6^{-6}}}\right)^{6-6-6}}{22}}\)

\(x^7+2x^6+3x^5+4x^4+3x^3+2x^2+x=\frac{19100}{3}\)

\(e\times\sqrt[12]{e^{\left({-3\times4}\right)}+5.67890}\)