Why must you always do the same thing to both sides of an equation

Question

anonymous · Answer

if it's an equation then left side equals right side. think of it like this: say you have a balance with two coins and you add 5 coins to one side.. it nolonger becomes equal so you add 5 coins to the other side to equal it out. doing the same thing to both sides

myininaya · Answer

3=3
does 
5+3=5+3 still hold?

myininaya · Answer

how about 3-4=3-4?

myininaya · Answer

3/5=3/5?
3*6=3*6?

myininaya · Answer

how about ln(3)=ln(3)
and 
3^2=3^2
and
3^3=3^3

myininaya · Answer

i notice how i have done the same thing to both sides
otherwise the lhs wouldn't be equal to the rhs
like if i done something to lhs of 3=3
and got 3^3=3
well that just isn't true since 27 does not equal 3