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StopWatch

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## Homework Statement

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.

## Homework 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!