1. The problem statement, all variables and given/known data The first: I was asked to evaluate (x^x)^(x^x) at f'(2). I tried to use logarithmic differentiation and ended up with a really messy left hand side of y's and y', while the right hand side was 1 + lnx + 1 + lnx. The right answer however is apparently 2^10(1 + ln2)(1 + 2ln2) and I'm not sure where I made my mistake. The Second: At noon, a bacteria culture has 200 bacteria. At 1 p.m., the bacteria population has grown to 800. I have to find the time where the population is 1800 assuming exponential growth. 2. Relevant equations The First: The relevant equations are above. The Second: I know m(t) = m(0)e^kt, so I have 800 = 200e^k1 but when I take the ln of both sides and solve for k (I got ln4) I end up with 1800 = 200e^ln4(t), which doesn't give me ln3/ln2 (the purported correct answer). I'm sure I'm just missing something very simple in both of these questions, but I really appreciate it. Thanks in advance!