# To_Poly_Solve_1

var("x")
 x
solve(x^x == 7, x, to_poly_solve=True)
 [x=log(7)W(log(7))]$\left[x=\frac{\mathrm{log}\left(7\right)}{\mathrm{W}\left(\mathrm{log}\left(7\right)\right)}\right]$
solve(x^3 + x^2 - x - 5 == 0, x, to_poly_solve=True)
 ⎡⎣⎢x=−12(2935−−√3–√+6227)13(i3–√+1)+2i3–√−29(2935−−√3–√+6227)13−13,x=−12(2935−−√3–√+6227)13(−i3–√+1)+−2i3–√−29(2935−−√3–√+6227)13−13,x=(2935−−√3–√+6227)13+49(2935−−√3–√+6227)13−13⎤⎦⎥$\left[x=-\frac{1}{2}\phantom{\rule{thinmathspace}{0ex}}{\left(\frac{2}{9}\phantom{\rule{thinmathspace}{0ex}}\sqrt{35}\sqrt{3}+\frac{62}{27}\right)}^{\frac{1}{3}}\left(i\phantom{\rule{thinmathspace}{0ex}}\sqrt{3}+1\right)+\frac{2i\phantom{\rule{thinmathspace}{0ex}}\sqrt{3}-2}{9\phantom{\rule{thinmathspace}{0ex}}{\left(\frac{2}{9}\phantom{\rule{thinmathspace}{0ex}}\sqrt{35}\sqrt{3}+\frac{62}{27}\right)}^{\frac{1}{3}}}-\frac{1}{3},x=-\frac{1}{2}\phantom{\rule{thinmathspace}{0ex}}{\left(\frac{2}{9}\phantom{\rule{thinmathspace}{0ex}}\sqrt{35}\sqrt{3}+\frac{62}{27}\right)}^{\frac{1}{3}}\left(-i\phantom{\rule{thinmathspace}{0ex}}\sqrt{3}+1\right)+\frac{-2i\phantom{\rule{thinmathspace}{0ex}}\sqrt{3}-2}{9\phantom{\rule{thinmathspace}{0ex}}{\left(\frac{2}{9}\phantom{\rule{thinmathspace}{0ex}}\sqrt{35}\sqrt{3}+\frac{62}{27}\right)}^{\frac{1}{3}}}-\frac{1}{3},x={\left(\frac{2}{9}\phantom{\rule{thinmathspace}{0ex}}\sqrt{35}\sqrt{3}+\frac{62}{27}\right)}^{\frac{1}{3}}+\frac{4}{9\phantom{\rule{thinmathspace}{0ex}}{\left(\frac{2}{9}\phantom{\rule{thinmathspace}{0ex}}\sqrt{35}\sqrt{3}+\frac{62}{27}\right)}^{\frac{1}{3}}}-\frac{1}{3}\right]$
z1(x) = x^5
z2(x) = 5^x
solve(z1(x) == z2(x), x, to_poly_solve=True)
 [x=−5W(−1205–√log(5)−120i25–√+10−−−−−−−−√log(5)+120log(5))log(5),x=−5W(1205–√log(5)−120i−25–√+10−−−−−−−−−√log(5)+120log(5))log(5),x=−5W(1205–√log(5)+120i−25–√+10−−−−−−−−−√log(5)+120log(5))log(5),x=−5W(−1205–√log(5)+120i25–√+10−−−−−−−−√log(5)+120log(5))log(5),x=−5W(−15log(5))log(5)]$\left[x=-\frac{5\phantom{\rule{thinmathspace}{0ex}}\mathrm{W}\left(-\frac{1}{20}\phantom{\rule{thinmathspace}{0ex}}\sqrt{5}\mathrm{log}\left(5\right)-\frac{1}{20}i\phantom{\rule{thinmathspace}{0ex}}\sqrt{2\phantom{\rule{thinmathspace}{0ex}}\sqrt{5}+10}\mathrm{log}\left(5\right)+\frac{1}{20}\phantom{\rule{thinmathspace}{0ex}}\mathrm{log}\left(5\right)\right)}{\mathrm{log}\left(5\right)},x=-\frac{5\phantom{\rule{thinmathspace}{0ex}}\mathrm{W}\left(\frac{1}{20}\phantom{\rule{thinmathspace}{0ex}}\sqrt{5}\mathrm{log}\left(5\right)-\frac{1}{20}i\phantom{\rule{thinmathspace}{0ex}}\sqrt{-2\phantom{\rule{thinmathspace}{0ex}}\sqrt{5}+10}\mathrm{log}\left(5\right)+\frac{1}{20}\phantom{\rule{thinmathspace}{0ex}}\mathrm{log}\left(5\right)\right)}{\mathrm{log}\left(5\right)},x=-\frac{5\phantom{\rule{thinmathspace}{0ex}}\mathrm{W}\left(\frac{1}{20}\phantom{\rule{thinmathspace}{0ex}}\sqrt{5}\mathrm{log}\left(5\right)+\frac{1}{20}i\phantom{\rule{thinmathspace}{0ex}}\sqrt{-2\phantom{\rule{thinmathspace}{0ex}}\sqrt{5}+10}\mathrm{log}\left(5\right)+\frac{1}{20}\phantom{\rule{thinmathspace}{0ex}}\mathrm{log}\left(5\right)\right)}{\mathrm{log}\left(5\right)},x=-\frac{5\phantom{\rule{thinmathspace}{0ex}}\mathrm{W}\left(-\frac{1}{20}\phantom{\rule{thinmathspace}{0ex}}\sqrt{5}\mathrm{log}\left(5\right)+\frac{1}{20}i\phantom{\rule{thinmathspace}{0ex}}\sqrt{2\phantom{\rule{thinmathspace}{0ex}}\sqrt{5}+10}\mathrm{log}\left(5\right)+\frac{1}{20}\phantom{\rule{thinmathspace}{0ex}}\mathrm{log}\left(5\right)\right)}{\mathrm{log}\left(5\right)},x=-\frac{5\phantom{\rule{thinmathspace}{0ex}}\mathrm{W}\left(-\frac{1}{5}\phantom{\rule{thinmathspace}{0ex}}\mathrm{log}\left(5\right)\right)}{\mathrm{log}\left(5\right)}\right]$