1. The problem is to solve the inequality $\log x \leq -10$. 2. Recall that $\log x$ usually means the logarithm base 10, so the inequality is $\log_{10} x \leq -10$. 3. The definition of logarithm tells us that $\log_{10} x = y$ means $x = 10^y$. 4. Applying this to the inequality, we rewrite it as $x \leq 10^{-10}$. 5. Also, remember the domain of $\log x$ is $x > 0$, so the solution must satisfy $0 < x \leq 10^{-10}$. 6. Therefore, the solution set is all $x$ such that $0 < x \leq 10^{-10}$. Final answer: $$0 < x \leq 10^{-10}$$