Solve x=T/3^n

$$x = \frac { T } { 3 ^ { n } }$$

Solve for T

$$T=x\times 3^{n}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{T}{3^{n}}=x$$

The equation is in standard form.

$$\frac{1}{3^{n}}T=x$$

Divide both sides by 3^{-n}.

$$\frac{\frac{1}{3^{n}}T\times 3^{n}}{1}=\frac{x\times 3^{n}}{1}$$

Dividing by 3^{-n} undoes the multiplication by 3^{-n}.

$$T=\frac{x\times 3^{n}}{1}$$

Divide x by 3^{-n}.

$$T=x\times 3^{n}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=-\frac{2\pi n_{1}i}{\ln(3)}-\log_{3}\left(\frac{x}{T}\right)\text{, }n_{1}\in \mathrm{Z}\text{, }&x\neq 0\text{ and }T\neq 0\\n\in \mathrm{C}\text{, }&x=0\text{ and }T=0\end{matrix}\right.$$

Solve for n

$$\left\{\begin{matrix}n=\log_{3}\left(\frac{T}{x}\right)\text{, }&\left(T<0\text{ and }x<0\right)\text{ or }\left(T>0\text{ and }x>0\right)\\n\in \mathrm{R}\text{, }&x=0\text{ and }T=0\end{matrix}\right.$$