<p>last second studier here. self studying the exam and I realize I don't know all the properties of ln and they keep coming up on questions. </p>
<p>Can someone summarize the important things I need to know about ln? i would really appreciate it. good luck to everyone tomorrow</p>
<p>You just have to remember that the derivative of ln f(x) is simply (1/f’(x))(1/f(x)), that the anti derivative of x^-1 is ln x, and that a^b=e^b*ln(a).</p>
<p>In addition, remember that
<p>If you have ln(u) and they ask for the derivative, it’s u’/u</p>
<p>If you have log(base a)x and they ask for the derivative, it’s lnx/lna. lna is a constant so you can rewrite it to read (1/lna)lnx, and then (remember ln(u) rule), so (1/lna)1/x </p>
<p>If you have a^u and they ask for the derivative, it’s (a^x)u’lna</p>
<p>I messed up in my response it should be (f’(x)/1)(1/f(x)) and not (1/f’(x))(1/f(x))</p>
<p>ln is the inverse function of e^x. This means cancellation properties apply so:</p>
<p>e^(ln x) = x
ln(e^x) = x</p>
<p>This is tested on the law of natural growth / decay, where you must solve for a constant k where dy/dt = ky</p>