$\log \sqrt{\frac{5}{3}}$

$\log \frac{5}{3}$

$\log \frac{4}{3}$

$\log \frac{2}{\sqrt{3}}$

3

0

1

infinitely many

$\sinh ^{-1}(\operatorname{cosec} \theta)$

$\sinh ^{-1}(\sec \theta)$

$\cosh ^{-1}(\operatorname{cosec} \theta)$

$\cosh ^{-1}(\sec \theta)$

$\left(0, \frac{\pi}{2}\right)$

$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$

$\left(-\frac{3 \pi}{4}, \frac{\pi}{4}\right)$

$\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$