Solve for x log of x- log of 22-x=1

Use the quotient property of logarithms, ${\displaystyle {\log }_b\left(x\right)-{\log }_b\left(y\right)={\log }_b\left(\frac{x}{y}\right)}$.

Rewrite ${\displaystyle \log \left(\frac{x}{22-x}\right)=1}$ in exponential form using the definition of a logarithm. If ${\displaystyle x}$ and ${\displaystyle b}$ are positive real numbers and ${\displaystyle b}$${\displaystyle \ne }$${\displaystyle 1}$, then ${\displaystyle {\log }_b\left(x\right)=y}$ is equivalent to ${\displaystyle b^y=x}$.

Cross multiply to remove the fraction.