If $\log_{b} a = c$, then $b^c = a$. Similarly, if $\log_{a} b = d$, then $a^d = b$.
Now, we want to prove that $\log_{b} a = \frac{1}{\log_{a} b}$. To do this, we can start by using the definition of logarithms:
$\log_{b} a = c \implies b^c = a$
$\log_{a} b =
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