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solve-x-x-1-4-How-can-we-get-the-complex-solution-




Question Number 148314 by Tawa11 last updated on 27/Jul/21
solve:      x^x    =   (1/4)  How can we get the complex solution
$$\mathrm{solve}:\:\:\:\:\:\:\mathrm{x}^{\mathrm{x}} \:\:\:=\:\:\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\mathrm{How}\:\mathrm{can}\:\mathrm{we}\:\mathrm{get}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{solution} \\ $$
Commented by Tawa11 last updated on 27/Jul/21
what is      W_n (− ln 4)
$$\mathrm{what}\:\mathrm{is}\:\:\:\:\:\:\mathrm{W}_{\mathrm{n}} \left(−\:\mathrm{ln}\:\mathrm{4}\right) \\ $$
Answered by Gbenga last updated on 27/Jul/21
x=e^(w(−ln(4)))
$$\boldsymbol{\mathrm{x}}=\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{w}}\left(−\boldsymbol{\mathrm{ln}}\left(\mathrm{4}\right)\right)} \\ $$

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