Diagonalization & Matrix Powers · Medium problem

Solve $\mathbf{x}'(t) = A\mathbf{x}(t)$ with $A = \begin{pmatrix}2 & 1\\1 & 2\end{pmatrix}$ and $\mathbf{x}(0) = \begin{pmatrix}3\\1\end{pmatrix}$. Find the first component $x_1(t)$ at $t = \ln 2$.