  Using the root adjunction formalism developed in an earlier work and
logarithmic THH, we obtain a simplified computation of $T(2)_*\text{K}(ku)$ for
$p>3$. Our computational methods also provide $T(2)_*\text{K}(ku/p)$, where
$ku/p$ is the $2$-periodic Morava $K$-theory spectrum of height $1$.

Algebraic Topology;K-Theory and Homology