Read about the history of logarithms.
See the Kahn Academy explain logarithms.
Think you got it? Test yourself here! Don't worry, there's no grade. This is just for fun. http://www.regentsprep.org/Regents/math/algtrig/ATE9/LogPrac.htm
Lastly, you can see just how well you know logarithmic equations. Check out this nifty interactive worksheet. http://www.themathpage.com/alg/logarithms.htm