logarithm equation with different bases. Why is this like it is? :D $$\dfrac{1}{\log_ae} = \ln(a)$$ I'm solving some exercises and I ran up to this? Maybe it's really banal, but please explain me...

We can prove $$\log_ab=\frac{\log_cb}{\log_ca}$$  where $a,c >0,\ne1$
$$\implies \log_ab\cdot\log_ba=\cdots=1$$
and conventionally Natural logarithm  is written as $\displaystyle \ln a$ which means $\displaystyle \log_ea$ 
