Question

Do you flip the inequality sign if you do the following:
1) Square root both sides
2) Exponentiate both sides by an odd number
3) Exponentiate both sides by an even numer
4) Cross-multiply
5) Log both sides

Answer 1

Any of one of them I meant, not doing all of them in chronological order.

Answer 2

If any process changes the sign of both sides, then yes. If the process changes the sign of only one side, then it depends (exponentiate with an even number, which I am reading as meaning raise to an even power).
If a process doesn't change a the sign, then no.
1) Square root both sides
must be positive, stays positive, no sign change
2) Exponentiate both sides by an odd number
sign doesn't change
3) Exponentiate both sides by an even numer
potential sign change, may or may not flip inequality
4) Cross-multiply
potential sign change, may or may not flip
5) Log both sides
must be positive, may become negative, may or may not flip

Answer 3

What do you mean by "if the processes changes the sign of only one side, it DEPENDS"