My solution to the problem is as follows:
69 = ((((6^2 * 10) + sqrt((5000*3) - 600)) / 4! ) * 4 ) - log(1 * 10^11)
Actually, there are a lot of equations that would yield to the number 69, I just made it complicated.
I hope my answer has come to your help. God bless and have a nice day ahead!