  In [Yan22a], we defined so-called ``log-type" GCD sums and proved the lower
bounds $\Gamma^{(\ell)}_1(N) \gg_{\ell} \left(\log\log N\right)^{2+2\ell}$. We
will establish the upper bounds $\Gamma^{(\ell)}_1(N)\ll_{\ell} \left(\log \log
N\right)^{2+2\ell}$ in this note, which generalizes G\'{a}l's theorem on GCD
sums (corresponding to the case $\ell = 0$). This result will be proved by two
different methods. The first method is unconditional. We establish sharp upper
bounds for spectral norms along $\alpha-$lines when $\alpha$ tends to $1$ with
certain fast rates. As a corollary, we obtain upper bounds for log-type GCD
sums. The second method is conditional. We prove that lower bounds for log-type
GCD sums $\Gamma^{(\ell)}_1(N)$ can produce lower bounds for large values of
derivatives of the Riemann zeta function on the 1-line. So from conditional
upper bound for $\left| \zeta^{(\ell)}\left(1+ i t\right)\right|$, we obtain
upper bounds for log-type GCD sums.
