Risolvi q^x=228

$$q ^ { x } = 228$$

Trova q (soluzione complessa)

$$q=e^{-\frac{2\pi n_{1}\left(Im(x)+iRe(x)\right)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\times 228^{\frac{Re(x)-iIm(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}$$

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

Trova x (soluzione complessa)

$$x=\frac{2\pi n_{1}i}{\ln(q)}+\log_{q}\left(228\right)$$

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

$$q\neq 1\text{ and }q\neq 0$$

Trova q

$$\left\{\begin{matrix}q=-228^{\frac{1}{x}}\text{, }&x\neq 0\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\\q=228^{\frac{1}{x}}\text{, }&x\neq 0\end{matrix}\right,$$

Trova x

$$x=\log_{q}\left(228\right)$$

$$q\neq 1\text{ and }q>0$$