  For a regular immersion of schemes $Z\to X$ and a cohomology theory of fs log
schemes, we formulate the logarithmic Gysin sequence using the "logarithmic
compactification" $(\mathrm{Bl}_Z X,E)$ instead of the open complement $X-Z$,
where $E$ is the exceptional divisor. We show that all $\mathbb{A}^1$-invariant
cohomology theories produced from motivic spectra and various non
$\mathbb{A}^1$-invariant cohomology theories like Nygaard completed prismatic
cohomology admit logarithmic Gysin sequences.
