The number of solutions of equation  $9^{1+\log x}-3^{1+\log x}-210=0$ (where base of log is 3) is

$9^{1+\log x}-3^{1+\log x}-210=0$

$9^1\cdot 9^{{\log }_{3}x}-3^1\cdot 3^{{\log }_{3}x}-210=0$

${9.3}^{2{\log }_{3}x}-3^1\cdot 3^{{\log }_{3}x}-210=0$

$9{\left(3^{{\log }_{3}x}\right)}^2-3\cdot 3^{{\log }_{3}x}-210=0$

Let  $3^{{\log }_{3}x}=z$

$\Rightarrow 9z^2-3z-210=0$

$\Rightarrow 3z^2-z-70=0\Rightarrow (z-5)(3z+14)=0$

$z=5$  (or)  $\frac{-14}{3}$

But  $z$ can’t be negative,

$\therefore z=5$

$3^{{\log }_{3}x}=5$

${\log }_{3}x={\log }_{3}5$

$\Rightarrow x=5$