Solucionar 2S^x=625

$$2 S ^ { x } = 625$$

Resolver para S (solución compleja)

$$S=e^{-\frac{2\pi n_{1}\left(Im(x)+iRe(x)\right)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\times 2^{\frac{-Re(x)+iIm(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\times 5^{\frac{4\left(Re(x)-iIm(x)\right)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}$$

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

Resolver para x (solución compleja)

$$x=\frac{2\pi n_{1}i}{\ln(S)}+\log_{S}\left(\frac{625}{2}\right)$$

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

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

Resolver para S

$$\left\{\begin{matrix}S=-\left(\frac{625}{2}\right)^{\frac{1}{x}}\text{, }&x\neq 0\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\\S=\left(\frac{625}{2}\right)^{\frac{1}{x}}\text{, }&x\neq 0\end{matrix}\right,$$

Resolver para x

$$x=\log_{S}\left(\frac{625}{2}\right)$$

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