Student or Learner
I tried taking him to the other side
I tried taking him the other side
I tried taking LOG to the base 10 to both sides
I tried taking LOG to base 10 both sides
Thanks in advance
----- I am not an ESL teacher -----
Regarding your first question, both forms seem to be correct. Although with "to" it is more complete, I guess you can omit it, as in your second version.
Now considering the second, independent, question, I think both forms sound a bit weird. I would say instead:
"I tried taking the log on both sides (the base 10 somewhat implied)."
"I tried taking the base ten logarithm on both sides."
"I tried taking the log on both sides (any practical base implied)."