7.126. $\log _{x} 9+\log _{x^{2}} 729=10$.
Solution.

Domain of definition: $\left\{\begin{array}{l}x>0, \\ x \neq \pm 1,\end{array} \quad 0<x \neq 1\right.$.

We have $\log _{x} 9+\frac{3}{2} \log _{x} 9=10, \log _{x} 9=4$, from which $x^{4}=9, x=\sqrt{3}$, $x=-\sqrt{3}$ does not fit the domain of definition.

Answer: $\sqrt{3}$.