• anonymous
what are logarithmic functions please try to explain
  • Stacey Warren - Expert
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
  • chestercat
I got my questions answered at in under 10 minutes. Go to now for free help!
  • shadowfiend
What do you mean exactly by `what are' they?
  • anonymous
It’s too hard to explain what logarithmic functions are in one sitting. It took me a while to understand them. And you can’t fully appreciate them until you learn what they really are at a deep level. But a logarithmic function, you can think of it as the inverse of the exponential function. For example, consider f(x) = e^x. That’s the exponential function. You can plug in values for x, and you get back values f(x). You can plug in x = 0, and you will get back f(0) = e^0 = 1. So (0, 1) is a point on f(x) = e^x. Plug some more in. Plug x = 1, and you get back f(1) = e^1 = e. (1, e) is a point on f(x). Plug x = 100, and you get f(100) = e^100. (100, e^100) is another point. Plug in x = -100, and you get back e^(-100). (-100, e^(-100)) is another point. If you try plug in all possible numbers into x for f(x) = e^x, you’ll see that you trace out a smooth, continuous curve that “grows exponentially.” The logarithmic functions are inverses of exponential functions. Let me call g(x) to be g(x) = log x, where the log has “base e,” the natural logarithm. Remember that (1, e) is a point on f(x)? Then (e, 1) is a point on g(x). That’s because g(e) = log (e) = 1. Similarly, since (100, e^100) is a point on f(x), we have (e^100, 100) is a point on g(x). That’s because g(e^100) = log (e^100) = 100 * log (e) = 100. Also, since (-100, e^(-100)) is a point on f(x), we have (e^(-100), -100) is a point on g(x). That’s because g(e^(-100)) = log (e^(-100)) = -100 * log (e) = -100. So if a point (a, b) is on f(x) = e^x, then the point (b, a) is on g(x) = log (x). So we see that they’re mirror images of each other. In fact, they’re mirror images across the line y = x since the x and y coordinates swapped. So e^x and log x are inverse functions not only because they “undo” each other, but also because they’re mirror images of each other across the line y = x. This helps us visualize log x, Graphically, inverse functions are mirror images of each other, reflected across the line y = x. So imagine drawing f(x) = e^x on a graph paper. Then draw in the line y = x. Fold your graph paper along the line y = x, and let f(x) = e^x be reflected across y = x. The reflection of e^x across the line y = x is just where the the curve e^x touches the graph paper when you folded it. That reflection is g(x) = log x.

Looking for something else?

Not the answer you are looking for? Search for more explanations.