y=2log(x) and y=log(x^2)

[Chazef]

hey the graphs y=2log(x) and y=log(x^2) are both from the same equation but clearly one will have the domain of R+ and the other will have R\{0} so when it comes to drawing graphs, are you not allowed to rearrange the graph to give a new domain or something because as I said they have are basically the exact same equation. Thanks

[e^1]

Just to be safe, since the domains are different in comparison to both equations, you should draw the one that the question directly states. Hence, do not rearrange the equation (in this case).

[lzxnl]

A function is defined by its rule AND its domain. The two functions y=2x+1, x E R and y=2x+1, x E R+ are different functions as their domains are not the same. Therefore, although the rules for y=2 ln x and y=ln x^2 coincide when x>0, they are not the same function and hence it would not be a good idea to switch between them. What you CAN do, however, is note in your mind that ln x^2 is an even function and that for x<0, its shape would be exactly the same as for y=2 ln x, just reflected.