2. Review:
How do you find the inverse of a function?
Application of what you know…
What is the inverse of f(x) = 3x?
y = 3x
x = 3y
y = log3x
f-1(x) = log3x
Rewrite the exponential as a logarithm…

3. Find the inverse of the following exponential functions…
f(x) = 2x f-1(x) = log2x
f(x) = 2x f-1(x) = log2x - 1
f(x) = 3x f-1(x) = log3(x + 1)

4. Find the inverse of the following logarithmic functions…
f(x) = log4x f-1(x) = 4x
f(x) = log2(x - 3) f-1(x) = 2x + 3
f(x) = log3x – f-1(x) = 3x+6

5. Graphs of Logarithmic Functions
Graph g(x) = log3x
It is the inverse of y = 3x
Therefore, the table of values for g(x) will be the reverse of the table of values for y = 3x.
y = 3x x y -1
1/3 1 3 2 9
y= log3x x y
1/3 -1 1 3 9 2 
Domain? (0,)  
Range? (-,) 
Asymptotes? x = 0

6. Graphs of Logarithmic Functions
g(x) = log4(x – 3)
What is the inverse exponential function?
y= 4x + 3
Show your tables of values.   
y= 4x + 3 x y -1
3.25 4 1 7 2 19
y= log4(x – 3) x y
3.25 -1 4 7 1 19 2
Domain? (3,)
Range? (-,)
Asymptotes? x = 3

7. Graphs of Logarithmic Functions
g(x) = log5(x – 1) + 4
What is the inverse exponential function?
y= 5x-4 + 1 
Show your tables of values.  
y= 5x-4 + 1 x y 3
1.2 4 2 5 6 26
y= log5(x – 1) + 4 x y
1.2 3 2 4 6 5 26
Domain? (1,)
Range? (-,)
Asymptotes? x = 1