Giải b^x=6561

$$b ^ { x } = 6561$$

Tìm b (complex solution)

$$b=e^{-\frac{2\pi n_{1}\left(Im(x)+iRe(x)\right)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\times 3^{\frac{8\left(Re(x)-iIm(x)\right)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}$$

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

Tìm x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(b)}+8\log_{b}\left(3\right)$$

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

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

Tìm b

$$\left\{\begin{matrix}b=-6561^{\frac{1}{x}}\text{, }&x\neq 0\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\\b=6561^{\frac{1}{x}}\text{, }&x\neq 0\end{matrix}\right,$$

Tìm x

$$x=8\log_{b}\left(3\right)$$

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