Couldbn't I say that
log (subscript b) a = log a / log b is true for any base/subscript.
Then 1 / [log (subscript a) b] = 1 / [log b / log a]
Where 1 / [log b / log a]
=log a / log b
Now use the fact at the top to change this into
log a / log b = log (subscript b) a
Therefore, 1 / [log (subscript a) b] = log (subscript b) a.
?