To_Poly_Solve_1 -- Sage

var("x")

solve(x^x == 7, x, to_poly_solve=True)

[x = \frac{\log (7)}{W (\log (7))}]

$\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \frac{\log\left(7\right)}{\operatorname{W}({\log\left(7\right)})}\right]$

solve(x^3 + x^2 - x - 5 == 0, x, to_poly_solve=True)

[x = - \frac{1}{2} {(\frac{2}{9} \sqrt{35} \sqrt{3} + \frac{62}{27})}^{\frac{1}{3}} (i \sqrt{3} + 1) + \frac{2 i \sqrt{3} - 2}{9 {(\frac{2}{9} \sqrt{35} \sqrt{3} + \frac{62}{27})}^{\frac{1}{3}}} - \frac{1}{3}, x = - \frac{1}{2} {(\frac{2}{9} \sqrt{35} \sqrt{3} + \frac{62}{27})}^{\frac{1}{3}} (- i \sqrt{3} + 1) + \frac{- 2 i \sqrt{3} - 2}{9 {(\frac{2}{9} \sqrt{35} \sqrt{3} + \frac{62}{27})}^{\frac{1}{3}}} - \frac{1}{3}, x = {(\frac{2}{9} \sqrt{35} \sqrt{3} + \frac{62}{27})}^{\frac{1}{3}} + \frac{4}{9 {(\frac{2}{9} \sqrt{35} \sqrt{3} + \frac{62}{27})}^{\frac{1}{3}}} - \frac{1}{3}]

$\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = -\frac{1}{2} \, {\left(\frac{2}{9} \, \sqrt{35} \sqrt{3} + \frac{62}{27}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{2 i \, \sqrt{3} - 2}{9 \, {\left(\frac{2}{9} \, \sqrt{35} \sqrt{3} + \frac{62}{27}\right)}^{\frac{1}{3}}} - \frac{1}{3}, x = -\frac{1}{2} \, {\left(\frac{2}{9} \, \sqrt{35} \sqrt{3} + \frac{62}{27}\right)}^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + \frac{-2 i \, \sqrt{3} - 2}{9 \, {\left(\frac{2}{9} \, \sqrt{35} \sqrt{3} + \frac{62}{27}\right)}^{\frac{1}{3}}} - \frac{1}{3}, x = {\left(\frac{2}{9} \, \sqrt{35} \sqrt{3} + \frac{62}{27}\right)}^{\frac{1}{3}} + \frac{4}{9 \, {\left(\frac{2}{9} \, \sqrt{35} \sqrt{3} + \frac{62}{27}\right)}^{\frac{1}{3}}} - \frac{1}{3}\right]$

z1(x) = x^5

z2(x) = 5^x

solve(z1(x) == z2(x), x, to_poly_solve=True)

[x = - \frac{5 W (- \frac{1}{20} \sqrt{5} \log (5) - \frac{1}{20} i \sqrt{2 \sqrt{5} + 10} \log (5) + \frac{1}{20} \log (5))}{\log (5)}, x = - \frac{5 W (\frac{1}{20} \sqrt{5} \log (5) - \frac{1}{20} i \sqrt{- 2 \sqrt{5} + 10} \log (5) + \frac{1}{20} \log (5))}{\log (5)}, x = - \frac{5 W (\frac{1}{20} \sqrt{5} \log (5) + \frac{1}{20} i \sqrt{- 2 \sqrt{5} + 10} \log (5) + \frac{1}{20} \log (5))}{\log (5)}, x = - \frac{5 W (- \frac{1}{20} \sqrt{5} \log (5) + \frac{1}{20} i \sqrt{2 \sqrt{5} + 10} \log (5) + \frac{1}{20} \log (5))}{\log (5)}, x = - \frac{5 W (- \frac{1}{5} \log (5))}{\log (5)}]

$\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = -\frac{5 \, \operatorname{W}({-\frac{1}{20} \, \sqrt{5} \log\left(5\right) - \frac{1}{20} i \, \sqrt{2 \, \sqrt{5} + 10} \log\left(5\right) + \frac{1}{20} \, \log\left(5\right)})}{\log\left(5\right)}, x = -\frac{5 \, \operatorname{W}({\frac{1}{20} \, \sqrt{5} \log\left(5\right) - \frac{1}{20} i \, \sqrt{-2 \, \sqrt{5} + 10} \log\left(5\right) + \frac{1}{20} \, \log\left(5\right)})}{\log\left(5\right)}, x = -\frac{5 \, \operatorname{W}({\frac{1}{20} \, \sqrt{5} \log\left(5\right) + \frac{1}{20} i \, \sqrt{-2 \, \sqrt{5} + 10} \log\left(5\right) + \frac{1}{20} \, \log\left(5\right)})}{\log\left(5\right)}, x = -\frac{5 \, \operatorname{W}({-\frac{1}{20} \, \sqrt{5} \log\left(5\right) + \frac{1}{20} i \, \sqrt{2 \, \sqrt{5} + 10} \log\left(5\right) + \frac{1}{20} \, \log\left(5\right)})}{\log\left(5\right)}, x = -\frac{5 \, \operatorname{W}({-\frac{1}{5} \, \log\left(5\right)})}{\log\left(5\right)}\right]$