Solve operatorname{lon}4^1+x+4^1-x=10

$$\operatorname { lon } 4 ^ { 1 + x } + 4 ^ { 1 - x } = 10$$

Solve for l (complex solution)

$$\left\{\begin{matrix}l=-\frac{2-5\times 4^{x}}{2no\times 16^{x}}\text{, }&n\neq 0\text{ and }o\neq 0\\l\in \mathrm{C}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}i}{\ln(2)}-\frac{\log_{2}\left(5\right)}{2}+\frac{1}{2}\text{ and }\left(\left(o=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}i}{\ln(2)}-\frac{\log_{2}\left(5\right)}{2}+\frac{1}{2}\right)\text{ or }n=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4^{1-x} from both sides.

$$lon\times 4^{1+x}=10-4^{1-x}$$

The equation is in standard form.

$$no\times 4^{x+1}l=10-4^{-x+1}$$

Divide both sides by on\times 4^{1+x}.

$$\frac{no\times 4^{x+1}l}{no\times 4^{x+1}}=\frac{2\left(5\times 4^{x}-2\right)}{4^{x}no\times 4^{x+1}}$$

Dividing by on\times 4^{1+x} undoes the multiplication by on\times 4^{1+x}.

$$l=\frac{2\left(5\times 4^{x}-2\right)}{4^{x}no\times 4^{x+1}}$$

Divide \frac{2\left(5\times 4^{x}-2\right)}{4^{x}} by on\times 4^{1+x}.

$$l=\frac{2\times 4^{-2x-1}\left(5\times 4^{x}-2\right)}{no}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=-\frac{2-5\times 4^{x}}{2lo\times 16^{x}}\text{, }&o\neq 0\text{ and }l\neq 0\\n\in \mathrm{C}\text{, }&\left(\left(l=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}i}{\ln(2)}-\frac{\log_{2}\left(5\right)}{2}+\frac{1}{2}\right)\text{ or }o=0\right)\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}i}{\ln(2)}-\frac{\log_{2}\left(5\right)}{2}+\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4^{1-x} from both sides.

$$lon\times 4^{1+x}=10-4^{1-x}$$

The equation is in standard form.

$$lo\times 4^{x+1}n=10-4^{-x+1}$$

Divide both sides by lo\times 4^{1+x}.

$$\frac{lo\times 4^{x+1}n}{lo\times 4^{x+1}}=\frac{2\left(5\times 4^{x}-2\right)}{4^{x}lo\times 4^{x+1}}$$

Dividing by lo\times 4^{1+x} undoes the multiplication by lo\times 4^{1+x}.

$$n=\frac{2\left(5\times 4^{x}-2\right)}{4^{x}lo\times 4^{x+1}}$$

Divide \frac{2\left(5\times 4^{x}-2\right)}{4^{x}} by lo\times 4^{1+x}.

$$n=\frac{2\times 4^{-2x-1}\left(5\times 4^{x}-2\right)}{lo}$$

Solve for l

$$\left\{\begin{matrix}l=-\frac{2-5\times 4^{x}}{2no\times 16^{x}}\text{, }&n\neq 0\text{ and }o\neq 0\\l\in \mathrm{R}\text{, }&x=\frac{-\log_{2}\left(5\right)+1}{2}\text{ and }\left(n=0\text{ or }o=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4^{1-x} from both sides.

$$lon\times 4^{1+x}=10-4^{1-x}$$

The equation is in standard form.

$$no\times 4^{x+1}l=10-4^{-x+1}$$

Divide both sides by on\times 4^{1+x}.

$$\frac{no\times 4^{x+1}l}{no\times 4^{x+1}}=\frac{2\left(5\times 4^{x}-2\right)}{4^{x}no\times 4^{x+1}}$$

Dividing by on\times 4^{1+x} undoes the multiplication by on\times 4^{1+x}.

$$l=\frac{2\left(5\times 4^{x}-2\right)}{4^{x}no\times 4^{x+1}}$$

Divide \frac{2\left(5\times 4^{x}-2\right)}{4^{x}} by on\times 4^{1+x}.

$$l=\frac{2\times 4^{-2x-1}\left(5\times 4^{x}-2\right)}{no}$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{2-5\times 4^{x}}{2lo\times 16^{x}}\text{, }&o\neq 0\text{ and }l\neq 0\\n\in \mathrm{R}\text{, }&x=\frac{-\log_{2}\left(5\right)+1}{2}\text{ and }\left(o=0\text{ or }l=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4^{1-x} from both sides.

$$lon\times 4^{1+x}=10-4^{1-x}$$

The equation is in standard form.

$$lo\times 4^{x+1}n=10-4^{-x+1}$$

Divide both sides by lo\times 4^{1+x}.

$$\frac{lo\times 4^{x+1}n}{lo\times 4^{x+1}}=\frac{2\left(5\times 4^{x}-2\right)}{4^{x}lo\times 4^{x+1}}$$

Dividing by lo\times 4^{1+x} undoes the multiplication by lo\times 4^{1+x}.

$$n=\frac{2\left(5\times 4^{x}-2\right)}{4^{x}lo\times 4^{x+1}}$$

Divide \frac{2\left(5\times 4^{x}-2\right)}{4^{x}} by lo\times 4^{1+x}.

$$n=\frac{2\times 4^{-2x-1}\left(5\times 4^{x}-2\right)}{lo}$$