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If your equation contains an exponential function or a logarithm function but cannot be brought to the form of equations (1) - (4), you could try to apply a predefined generalization of Lambert W.
See e.g. [Corcino/Corcino/Mezö 2017], [Dubinov/Galidakis 2007], [Galidakis 2005], [Maignan/Scott 2016], [Mezö 2017], [Barsan 2018].
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[Barsan 2018] Barsan, V.: Siewert solutions of transcendental equations, generalized Lambert functions and physical applications. Open Phys. 16 (2018) 232–242

[Maignan/Scott 2016] Maignan, A.; Scott, T. C.: Polynomial-Exponential and Generalized Lambert Function. 2016

[Mezö/Baricz 2017] Mezö, I.; Baricz, A.: On the generalization of the Lambert W function. Transact. Amer. Math. Soc. 369 (2017) (11) 7917–7934

If your equation contains an exponential function or a logarithm function but cannot be brought to the form of equations (1) - (4), you could try to apply a predefined generalization of Lambert W.
See e.g. [Corcino/Corcino/Mezö 2017], [Dubinov/Galidakis 2007], [Galidakis 2005], [Maignan/Scott 2016], [Mezö 2017], [Mezö/Baricz 2017], [Barsan 2018], [Castle 2018].
$\ $

[Barsan 2018] Barsan, V.: Siewert solutions of transcendental equations, generalized Lambert functions and physical applications. Open Phys. 16 (2018) 232–242

[Castle 2018] Castle, P.: Taylor series for generali-zed Lambert W functions. 2018

[Maignan/Scott 2016] Maignan, A.; Scott, T. C.: Polynomial-Exponential and Generalized Lambert Function. 2016

[Mezö 2017] Mezö, I.: On the structure of the solution set of a generalized Euler-Lambert equa-tion. J. Math. Anal. Appl. 455 (2017) (1) 538-553

[Mezö/Baricz 2017] Mezö, I.; Baricz, A.: On the generalization of the Lambert W function. Transact. Amer. Math. Soc. 369 (2017) (11) 7917–7934 (On the generalization of the Lambert W function with applications in theoretical physics. 2015)

See also [Edwards 2020], [Galidakis/ Weisstein], [Köhler].

See also [Edwards 2020], [Galidakis/Weisstein], [Köhler].

Assume an ordinary equation $F(x)=c$ is given where $c$ is a constant and $F$ is a function. Isolating $x$ on one side of the equation only by operations to the whole equation means to apply a suitable local inverse function (branch of the inverse relation) $F^{-1}$ of $F$: $\ x=F^{-1}(c)$.

Assume an ordinary equation $F(x)=c$ is given where $c$ is a constant and $F$ is a function. Isolating $x$ on one side of the equation only by operations to the whole equation means to apply a suitable partial inverse function (branch of the inverse relation) $F^{-1}$ of $F$: $\ x=F^{-1}(c)$.