# Problems in $\textbf{DSPACE}(\log^2 n)$

Let some problem $$P$$ is in $$\textbf{DSPACE}(\log^2 n)$$ and $$Q$$ is a problem in $$\textbf{DSPACE}(\log n)$$. I can claim that $$P$$ is polynomial time solvable as number of turing machine configurations for problem $$Q$$ is polynomial many.

Question : Can I say that $$\textbf{DSPACE}(\log^2 n)$$ is in polynomial time complexity class?

There are about $$2^{\log^2n}$$ possible configurations, and $$2^{\log^2n} = n^{\log n}$$, which is not polynomial (it's "quasipolynomial"). So, no, you can't claim that $$\mathrm{DSPACE}[\log^2 n]\subseteq \mathrm{P}$$.