35. $\log _{\frac{1}{3}} \log _{5}\left(\sqrt{x^{2}+1}+x\right)<\log _{3} \log _{\frac{1}{3}}\left(\sqrt{x^{2}+1}-x\right)$.
35. In both parts of the inequality, we switch to the base 3 and 5.

The inequality will take the form $2 \log _{3} \log _{5}\left(\sqrt{x^{2}+1}+x\right)>0$.

From which $\log _{5}\left(\sqrt{x^{2}+1}+x\right)>1, \sqrt{x^{2}+1}+x>5$. Answer: $x>\frac{12}{5}$.