Consider the following feature transform, which maps a d-dimensional $x$ to a one-dimension $z$, keeping only the $k$th coordinate of $x$
$\phi_{(k)}(x)=(1,x_k)$
Let $H_k$ be the set of perceptrons in the feature space.
Prove that $d_{vc}(\cup_{k=1}^dH_k) \leq 2(\log_2d+1)$.
I have no idea about this question, for I do not know how to introduce the $\log_2$ int my inequality.