다음을 풀어보세요: y=(a-4)^x

$$y = ( a - 4 ) ^ { x }$$

a에 대한 해 (complex solution)

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

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

x에 대한 해 (complex solution)

$$\left\{\begin{matrix}x=\frac{2\pi n_{1}i}{\ln(a-4)}+\log_{a-4}\left(y\right)\text{, }n_{1}\in \mathrm{Z}\text{, }&y\neq 0\text{ and }a\neq 5\text{ and }a\neq 4\\x\in \mathrm{C}\text{, }&\left(a=4\text{ and }y=0\right)\text{ or }\left(a=5\text{ and }y=1\right)\end{matrix}\right.$$

x에 대한 해

$$\left\{\begin{matrix}x=\log_{a-4}\left(y\right)\text{, }&y>0\text{ and }a\neq 5\text{ and }a>4\\x\in \mathrm{R}\text{, }&\left(a=5\text{ and }y=1\right)\text{ or }\left(a=3\text{ and }y=-1\text{ and }Denominator(x)\text{bmod}2=1\text{ and }Numerator(x)\text{bmod}2=1\right)\\x>0\text{, }&a=4\text{ and }y=0\end{matrix}\right.$$