In brief, it is because it was designed to. The purposes of log and ln is to solve for exponents. log generally without a base written by it is base 10. ln is log base e. so if you ask why does ln(e) cancel out… it is not that it cancels out, it is that the answer is 1. What you actually are asking when you write ln(e) is e^x=e and the answer is 1 so ln(e) is = 1. Great and interesting question. Thanks.