# Exponential and Logarithmic Functions

1. An example of an exponential function is y=8^x. Convert this exponential function to a logarithmic function. Plot the graph of both the functions.

2. Graph these two functions

? An exponential function f(x)=6x-2

? A logarithmic function f(x)=log9x

3. Look at the graphical representation below and derive quadratic and linear equations from it.

[see attachment]

I am trying to learn the process of different functions and equations. Please show work as much as possible.

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#### Solution Preview

1. An example of an exponential function is y=8x Convert this exponential function to a logarithmic function. Plot the graph of both the functions.

An exponential function and a logarithmic function are basically the same thing - just written in different ways. If you have an exponential relationship a = bc, this can be rewritten as logb(a) = c.

Similarly, y = 8x can be written as log8(y) = x. If you graph these, they will look exactly the same, since they are the same equation ...