There seem to be different interpretations of this question.
(1) Assuming the expression is log(K(X+A))+B:
Let y=log(K(X+A))+B, and B=pK where p is a constant.
y=log(K(X+A))+pK.
(0,0): 0=log(KA)+pK;
(3,5): 5=log(3K+KA)+pK.
So, 5=log(3K+KA)-log(KA)=log((3K+KA)/KA)=log(3/A+1).
3/A+1=105 or e5 depending on the log base being 10 or e. Assume base e (natural log).
3/A=e5-1, A=3/(e5-1).
-pK=ln(3K/(e5-1)).
If K=1, p=-ln(3/(e5-1))=ln((e5-1)/3).
p=B/K=ln((e5-1)/3)/K, B=ln((e5-1)/3). So we found A and B, but we can't find K, because all we know is that B changes with K so that B/K is a constant.
(2) Assuming the expression is logK(X+A)+B: let y=logK(X+A)+B.
(0,0): 0=logK(A)+B, B=logK(1/A);
(3,5): 5=logK(3+A)+B.
5=logK(3/A+1), K5=3/A+1, 3/A=K5-1, A=3/(K5-1), B=logK((K5-1)/3).