Riješi q^x+1=sqrt[3]{3}

$$q ^ { x + 1 } = \sqrt[ 3 ] { 3 }$$

Izračunaj q (complex solution)

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

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

Izračunaj x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(q)}+\frac{\log_{q}\left(3\right)}{3}-1$$

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

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

Izračunaj q

$$\left\{\begin{matrix}q=-3^{\frac{1}{3\left(x+1\right)}}\text{, }&x\neq -1\text{ and }Numerator(x+1)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\\q=3^{\frac{1}{3\left(x+1\right)}}\text{, }&x\neq -1\end{matrix}\right,$$

Izračunaj x

$$x=\frac{\log_{q}\left(3\right)-3}{3}$$

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