1) Logarithms translate a log statement into an exponential statement with the same base. 2) To translate a log statement, identify the base, power, and starting number. 3) Examples show translating log statements to exponential statements using a calculator to evaluate.

1. Block 3
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. y = 4x
y = x
y = log4x
1
(2 , )16
1
(16 , 2)

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

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

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

8. Using Logs
10
t
log10 1000 = t
1000 =
t = 3
r
3
logr 8 = 3
8 =
r = 2

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

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

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

12. r
6
logr 1000000 = 6
1000000 =
r = 10

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

14. f
3
logf 125 = 3
125 =
f = 5
Key Question
Solve