  We prove potential automorphy results for a single Galois representation $G_F
\rightarrow GL_n(\overline{\mathbb{Q}}_l)$ where $F$ is a CM number field. The
strategy is to use the $p,q$ switch trick and modify the Dwork motives employed
in \cite{HSBT} to break self-duality of the motives, but not the Hodge-Tate
weights. Another key result to prove is the ordinarity of certain $p$-adic
representations, which follows from log geometry techniques. One input is the
automorphy lifting theorem in \cite{tap}.
