1. Logarithms

2. What is to be learned?
How to translate a log statement

3. Previously
Exponentials are in form y = ax
Logs are their inverse

4. (2 , ) 16
y = 4x
y = x
y = log4x 1
(16 , 2) 1

5. y = log4x
y = logax
2 = log416
x = ay
42 = 16
y = log4x
(16 , 2)
(x , y) 1

6. x a statement logax = y translation x = a (starting no.)
(power)
(power) a
(base)
(base)
(base)

7. Using Logs
log2 x = 4 4
x = 2
x = 16
log5 x = 3 3
x = 5
x = 125

8. Using Logs
log = t t
1000 = 10
t = 3
logr 8 = 3 3 r
8 =
r = 2

9. Using Calculator log10 1000 = x 1000 = 10 x = 3 log log = ln
(natural log) e

10. Logarithms starting no. statement logax = y power base translation x =

11. Using Logs
log7 x = 3 3
x = 7
x = 343
log5 625 = h h
625 = 5
x = 4

12. logr = 6 6 r =
r = 10

13. On Calculator
log
is log 10
log
is ln
(natural log) e