Originally Posted by
plato let's use the standard notation for natural logarithm, $\log(x)$.
Now $\log_b(a)=\dfrac{\log(a)}{\log(b)}~\&~\log_b(c)= \dfrac{\log(c)}{\log(b)}$
then is it true that $\log(c)\dfrac{\log(a)}{\log(b)}=\log(a)\dfrac{ \log(c)}{\log(b)}~?$