Leysa a^x=12

$$a ^ { x } = 12$$

Leystu fyrir a (complex solution)

$$a=e^{-\frac{2\pi n_{1}\left(Im(x)+iRe(x)\right)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\times 12^{\frac{Re(x)-iIm(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}$$

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

Leystu fyrir x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(a)}+\log_{a}\left(12\right)$$

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

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

Leystu fyrir a

$$\left\{\begin{matrix}a=-12^{\frac{1}{x}}\text{, }&x\neq 0\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\\a=12^{\frac{1}{x}}\text{, }&x\neq 0\end{matrix}\right.$$

Leystu fyrir x

$$x=\log_{a}\left(12\right)$$

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