$\text{If the product of all solutions of the equation}$
$\frac{\left(2019\right)x}{2020}=(2019{)}^{{\log }_x\left(2020\right)}$
$\text{can be expressed in the lowest form as}\frac{m}{n}$, $\text{then the value of}m-n\text{is}$

The correct option is B $1$
Given :
$\frac{\left(2019\right)x}{2020}=(2019{)}^{{\log }_x\left(2020\right)}$

$\text{Take log to the base}x\text{on both the sides}$

$\Rightarrow {\log }_x\left(2019\right)+1-{\log }_{x}2020={\log }_{x}2020\cdot {\log }_{x}2019$

$\Rightarrow {\log }_x\left(2019\right)[1-{\log }_{x}2020]+(1-{\log }_{x}2020)=0$

$\Rightarrow ({\log }_{x}2019+1)(1-{\log }_{x}2020)=0\Rightarrow x=\frac{1}{2019}\text{(or)}x=2020\Rightarrow \text{Product of values of}x=\frac{2020}{2019}=\frac{m}{n}$
$\Rightarrow m-n=1$
Hence the correct answer is Option B.