I was doing a time complexity problem, and the solution mentioned that there is a single class for logs. Ie. we can write $\log_a (x) = \Theta(\log_b(x))$ where $a$ is not equal to $b$.
This can be done because apparently logs are all multiples of each other:
$\log_a (x) = \log_b (x) \cdot \log_a (b)$
So we will always achieve:
$\lim_{x\to \infty} \frac{\log_a (x)}{\log_b(x)} = \text{some constant}$; where $0 < \text{some constant} < \infty$, thus we can use $\Theta$.
My question is how is it clear that $\log$s are all multiples of each other? How does $\log_a (x) = \log_b (x) \cdot \log_a (b)$ demonstrate this?