SOLUTION: How are logarithmic functions related to exponential functions? Describe the basic properties of a logarithmic function. Describe at least two applications of logarithmic functions

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Question 948442: How are logarithmic functions related to exponential functions? Describe the basic properties of a logarithmic function. Describe at least two applications of logarithmic functions. What makes these applications logarithmic in nature?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
A way to answer your first question is to look at the roles of the dependant and independent variables, x and y.

b%5Ex=y

Reflect this in the line y=x, meaning switch roles of x and y, gives this equation:

b%5Ey=x
What do you do if you want THIS equation expressing y as a function of x? The number properties learned in Algebra 1 do not help too much for solving this as y in terms of x.


Just for example, let b=2.
Consider 2%5Ex=y shown in red, and 2%5Ey=x shown in green:
graph%28300%2C300%2C-8%2C16%2C-8%2C16%2C2%5Ex%2Clog%282%2Cx%29%29


Think about that for a few minutes, and then study from your book about exponential functions and their inverses. Your other three questions you will be ready for after you have done the proper study from your book about exponential functions and their inverses.