Question

How can exponential and logarithmic functions be combined

Answer 1

Well.. .not exactly what you're asking, but the relationship of them is 
${ log_{{ a}}{{ b}}=y \iff {{ a}}^y={{ b}}\qquad\qquad % exponential notation 2nd form {{ a}}^y={{ b}}\iff log_{{ a}}{{ b}}=y }$

so... hmm to add some
for example  let's say   $if\ 5^3=125\textit{ that can be written also as} \\ \quad \\ log_5(125)=3$