1. Inverses of Exponential Functions
March 23, 2016

2. One Minute Question
If f(x) = 3x – 4, find f-1(5)
This means f(x) = 5, so
3x – 4 = 5
3x = 9
x=2

3. So What Do We Do With Exponential Inverses?
What is the parent exponential function?
f(x) = bx or y = bx
How do you find an inverse?
x = by
And then solve for y…, So

4. We create the logarithm.
Important definition!!!
If x = by,
then y = logb x

5. Logs are Exponents!
If a = bc,
then c = logb a

6. The base of the exponent is the base of the log.
The exponent becomes the actual logarithm.
The base of the exponent is the base of the log.
And the result of the power is what you take the log of. 3 3 2 2 8 8 = N x
log = b

7. Let’s Practice!!! If 43 = 64, then… log4 64 = 3 If 251/2 = 5, then…

8. Let’s practice by finding the simplest value for x:
log8 64 = x
log9 3 = x
log6 x = 3
log7 x = -1
logx 16= 4
logx 8 = -3
x = 2
x = 1/2
x = 216
x = 1/7

9. Let’s practice by finding x.
log8 85 = x
It equals 5 . Why??
log = x
It equals Why?

10. It’s calculator time! Press the log button. What happens?
What base do you think this is?
How could you find out?
Find log 100.
Find log
Find log 2. What does this mean?
It should be 2.
It should be -5.

11. It’s calculator time! Can we find logs in other bases. How?
If you don’t have that function
on your calculator, use the
change of base property:
logb n = (log n)/(log b)
so log2 8 = (log 8)/(log 2)

12. Assignment:

13. Test Tomorrow ! Questions!
If f(x) = 3x – 5, g(x) = (x -2) and h(x) = 4x – 2,
The vertex of g(x).
The vertex of f(g(x)).
The vertex of (g◦f)(x).
The asymptote of h(x).
The asymptote of f(h(x)).

14. Test Tomorrow ! Questions!
If f(x) = 3x – 5, g(x) = (x -2) and h(x) = 4x – 2,
The roots of (f∙g)(x).
The value of (f + g)(4) – h(2).

15. More Questions If fuctions f, g, and h are given by this table:
Find (f – h)(3).
Find (g/h)(1).
Which functions are one-to-one?
Find h(f-1(g(3))). x 1 2 3 4 5 f 7 g h

16. More Questions If fuctions f and g are given by these graphs:
Approximate
(f + g)(3).
(f∙g)(-2).
Sketch g-1(x).
Write the function f(x).