If  ${\log }_{10}(x-9)+{\log }_{10}x=1$, then  $x=$

${\log }_{10}(x-9)+{\log }_{10}x=1$

${\log }_{10}x(x-9)=1$

$x(x-9)=10$

$x^2-9x-10=0$

$x^2-10x+x-10=0$

$x(x-10)+1(x-10)=0$

$(x-10)(x+1)=0$

$x=10\left(\text{or}\right)x=-1;\text{\hspace{0.17em}but\hspace{0.17em}}x=10$