When x → 0, Lim {lncos2x / lncos3x} = Lim {(lncos2x) '/ (lncos3x)'} = Lim {2tan2x / 3tan3x} The specific steps of (lncos2x) '= 2tan2x

(lncos2x )'=1/cos2x *(-sin2x)*2=-2tan2x
(lncos3x)'=1/cos3x *(-sin3x)*3=-3tan3x

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