You may never have personally experienced an earthquake, but you have seen or heard news reports where earthquakes are rated according to the Richter scale.
And, you’ve been exposed to sound levels being expressed in terms of decibels.
You may have also heard of acids and bases being measured in terms of a pH scale.
All are examples of the use of logarithms. Logarithms provide a way to turn back the effect of exponential scales.
This is because logarithms are another way to use exponents. A common definition of logarithms is in terms of exponents.
In terms of functions, the inverse of an exponential function is a logarithmic function with the same base.
Because of the properties of logarithms, it suffices to examine functions of the form f of x equals a plus n times the log base b of x minus c to understand all of the ways a logarithmic function can be modified.
This simulation allows you to experiment with logarithmic functions.
You can adjust any of the four parameters by using the sliders or by entering values directly into the entry fields.
The value b = 1 is not allowed for logarithms, and the value n = 0 has also been disabled.
A special value for the base of a logarithm is = e ≈ 2.7182818459… . A button is supplied to set the base equal to this value without having to enter it yourself.
So, experiment with the parameters a, b, c, and n. See what you can find out. Try to make a prediction about the effect of different values for a parameter before checking it. Good luck and good learning! 1