I've found the value for K using Gibbs free-energy values (in KJ/mol) where Gibbs free-energy = -5.707*log(K).
Would that mean the units of K are KJ/mol as well?
Are you asking whether in a formula
[tex]A = \log B[/tex]
units of A and B are identical? No, they are not.
What is the exact formula you have used? Or, in other words, where does the -5.707 constant comes from? What are its units?
Can you take log of something that has units? What is the result of such operation?
Write several (random) reaction equations and try to find the units of K. Do you see J (or kJ) there?