Rešite 3=ax^a

$$3 = a x ^ { a }$$

Rešitev za x (complex solution)

$$x=e^{-\frac{2\pi n_{1}iRe(a)}{\left(Re(a)\right)^{2}+\left(Im(a)\right)^{2}}-\frac{2\pi n_{1}Im(a)}{\left(Re(a)\right)^{2}+\left(Im(a)\right)^{2}}+\frac{arg(\frac{1}{a})Im(a)+iarg(\frac{1}{a})Re(a)}{\left(Re(a)\right)^{2}+\left(Im(a)\right)^{2}}}\times \left(\frac{3}{|a|}\right)^{\frac{Re(a)-iIm(a)}{\left(Re(a)\right)^{2}+\left(Im(a)\right)^{2}}}$$

$$n_{1}\in \mathrm{Z}$$

$$a\neq 0$$

Rešitev za x

$$\left\{\begin{matrix}x=\left(\frac{3}{a}\right)^{\frac{1}{a}}\text{, }&\left(Numerator(a)\text{bmod}2=1\text{ and }Denominator(a)\text{bmod}2=1\text{ and }a<0\right)\text{ or }\left(\left(\frac{3}{a}\right)^{\frac{1}{a}}>0\text{ and }a>0\right)\text{ or }\left(\left(\frac{3}{a}\right)^{\frac{1}{a}}<0\text{ and }Denominator(a)\text{bmod}2=1\text{ and }a>0\right)\\x=-\left(\frac{3}{a}\right)^{\frac{1}{a}}\text{, }&\left(Numerator(a)\text{bmod}2=1\text{ and }a<0\text{ and }Numerator(a)\text{bmod}2=0\text{ and }Denominator(a)\text{bmod}2=1\right)\text{ or }\left(\left(\frac{3}{a}\right)^{\frac{1}{a}}>0\text{ and }Numerator(a)\text{bmod}2=0\text{ and }Denominator(a)\text{bmod}2=1\text{ and }a>0\right)\text{ or }\left(\left(\frac{3}{a}\right)^{\frac{1}{a}}<0\text{ and }Numerator(a)\text{bmod}2=0\text{ and }a>0\right)\end{matrix}\right,$$