1) Mess around. See what you can figure out on your own.[br]2) Reset the applet and look for the following:[br] a. The left number line includes positive and negative numbers.[br] b. The right number line consists of only positive numbers.[br] c. As you move either blue point, which parts of the exponential expression (green) change? Which parts stay the same?[br] d. As you move either blue point, which parts of the logarithmic expression (purple) change? Which parts stay the same?[br] e. Move the left point to the "additive identity", 0. What does it match to on the right?[br] f. With all the boxes checked, verify in a few examples that *adding* numbers on the left number line corresponds to *multiplying* numbers on the right number line. This can be summarized by saying: "An exponential function turns addition into multiplication, while a logarithm turns multiplication into addition."[br][br]It's true that any exponential function y=b^x (where b>0 and b isn't 1) is a "correspondence" (a.k.a. "bijection", a.k.a. "one-to-one and onto map") between the set of all real numbers and the set of positive real numbers; however, I hope that by playing with this applet you find that there's something deeper going on.