다음을 풀어보세요: 1300000000=267x^0.352y

$$1300000000=267 { x }^{ 0.352y }$$

x에 대한 해 (complex solution)

$$x=e^{-\frac{15625\pi n_{1}\times \frac{88Im(y)+i\times 88Re(y)}{125}}{1936\left(\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}\right)}}\times \frac{1300000000}{267}^{\frac{-i\times 125Im(y)+125Re(y)}{44\left(\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}\right)}}$$

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

y에 대한 해 (complex solution)

$$y=\frac{i\times 125\pi n_{1}}{22\ln(x)}-\frac{125\log_{x}\left(\frac{267}{1300000000}\right)}{44}$$

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

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

x에 대한 해

$$\left\{\begin{matrix}x=-\frac{1300000000}{267}^{\frac{125}{44y}}\text{, }&y\neq 0\text{ and }Numerator(\frac{44y}{125})\text{bmod}2=0\text{ and }Denominator(\frac{44y}{125})\text{bmod}2=1\\x=\frac{1300000000}{267}^{\frac{125}{44y}}\text{, }&y\neq 0\end{matrix}\right.$$

y에 대한 해

$$y=-\frac{125\log_{x}\left(\frac{267}{1300000000}\right)}{44}$$

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