Solve ln^10=x

$$l { n }^{ 10 } =x$$

Solve for l (complex solution)

$$\left\{\begin{matrix}l=\frac{x}{n^{10}}\text{, }&n\neq 0\\l\in \mathrm{C}\text{, }&x=0\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$n^{10}l=x$$

Divide both sides by n^{10}.

$$\frac{n^{10}l}{n^{10}}=\frac{x}{n^{10}}$$

Dividing by n^{10} undoes the multiplication by n^{10}.

$$l=\frac{x}{n^{10}}$$

Solve for l

$$\left\{\begin{matrix}l=\frac{x}{n^{10}}\text{, }&n\neq 0\\l\in \mathrm{R}\text{, }&x=0\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$n^{10}l=x$$

Divide both sides by n^{10}.

$$\frac{n^{10}l}{n^{10}}=\frac{x}{n^{10}}$$

Dividing by n^{10} undoes the multiplication by n^{10}.

$$l=\frac{x}{n^{10}}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n\in e^{\frac{\pi i}{5}}l^{-\frac{1}{10}}\sqrt[10]{x},l^{-\frac{1}{10}}\sqrt[10]{x},e^{\frac{2\pi i}{5}}l^{-\frac{1}{10}}\sqrt[10]{x},e^{\frac{3\pi i}{5}}l^{-\frac{1}{10}}\sqrt[10]{x},e^{\frac{4\pi i}{5}}l^{-\frac{1}{10}}\sqrt[10]{x},-l^{-\frac{1}{10}}\sqrt[10]{x},e^{\frac{6\pi i}{5}}l^{-\frac{1}{10}}\sqrt[10]{x},e^{\frac{7\pi i}{5}}l^{-\frac{1}{10}}\sqrt[10]{x},e^{\frac{8\pi i}{5}}l^{-\frac{1}{10}}\sqrt[10]{x},e^{\frac{9\pi i}{5}}l^{-\frac{1}{10}}\sqrt[10]{x}\text{, }&l\neq 0\\n\in \mathrm{C}\text{, }&x=0\text{ and }l=0\end{matrix}\right.$$

Solve for n

$$\left\{\begin{matrix}n=\sqrt[10]{\frac{x}{l}}\text{; }n=-\sqrt[10]{\frac{x}{l}}\text{, }&\left(x\geq 0\text{ and }l>0\right)\text{ or }\left(x\leq 0\text{ and }l<0\right)\\n\in \mathrm{R}\text{, }&x=0\text{ and }l=0\end{matrix}\right.$$