Which one is correct??

[I'm still learning]

I tried taking him to the other side

or

I tried taking him the other side


Similarly,

I tried taking LOG to the base 10 to both sides

or

I tried taking LOG to base 10 both sides


Thanks in advance

 

[Abstract Idea]

----- I am not an ESL teacher -----

I tried taking him to the other side

or

I tried taking him the other side


Similarly,

I tried taking LOG to the base 10 to both sides

or

I tried taking LOG to base 10 both sides


Thanks in advance

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)."
or
"I tried taking the base ten logarithm on both sides."
or
"I tried taking the log on both sides (any practical base implied)."