Do these two complexities belong in the same theta class?

Question

Do $n\log_d(n)$ and $n\log(n)$ lie in the same theta class?

Answer 1

Yes, due to the identity $\log_b x=\dfrac{\log_a x}{\log_a b}$ (for $a,b\in\Bbb R^+\setminus\{1\},\ x\in\Bbb R^+$).