If you have trouble making sure they're equal, an important thing to do is to check with some value of x.
Such as:
e = ln(2), with x = 1
I'd suggest you check what the actual problem is with the textbook or worksheet it originated from. Also, if you meant e^x = ln((x+1)^(1/x)), make sure your syntax is correct when typing a problem.
The way I typed it was the way my friend typed it to me ): I checked ln((x+1)^(1/x)), but it's also not equal to e^x :/ Thanks for all your help guys! :D