how does one go about using log table to solve (2.874^2)+6//(2.874^2)+6 ?

those pesky +6 terms pretty much get in the way of using logs to help.

log(ab) = loga + logb
But log(a+b) cannot be simplified like that.

and did you mean to repeat (2.874^2)+6 ??
And what's with the // operator?