They work the same way as each other ...
You can express exponential equations using logarithms and vice versa:
logb(expression) = number ... means the same thing as bnumber = (expression).
What I tell my students is to remember to keep the bases the same, and the exponent of the base stands alone in the logarithmic expression.
Example: log5(25) = 2 means the same thing as 52 = 25
With natural logarithms (where the base is an understood e), you do the same thing...
Example: ln (4) = 1.3863 means the same thing as e1.3863 = 4
Hope this helps you.