1. Logarithms

2. ??
?? LOGARITHM ??
??

3. Inverse Functions
• Original function: y = kx => f (x) = kx
• Inverse function:
x
x
-1
x = ky => y = => f (x) =
k
k

4. Example
x
f (x) = 2x;f (x) =
2
-1

5. Inverses Invert
x
g(x) =
2
f (x) = 2x
(
æ xö
f  g (x) = 2 ç ÷ = x
è 2ø
(
2x
g  f (x) =
=x
x
)
)

6. y =k
Invert y = k x:
x =k
y
Now solve for y.
x

7. ???????????
?????????????

8. Enter the Logarithm
()
loga b = c
means
a =b
c
“Jumping Horse Outline”by warszawianka. Found at
http://openclipart.org/detail/10712/jumping-horse-outline-bywarszawianka-10712. Public domain.

9. x =k
Solution:
y
y = logk x

10. ()
loga b = c

a =b
c
Implications? Graphs of inverse functions reflect
over line y = x

11. Implications
•
•
•
•
Increasing
Asymptote: y-axis => x>0.
loga1=0.
logaa=1.

12. Summary
Basic relationship:
y = a <=> x = loga y
x

13. Next
Yes but so what?