1. Logarithms – making complex calculations easy
John Napier
John Wallis
Johann Bernoulli
Jost Burgi

2. Introduction to Logarithmic Functions
GRAPHS OF EXPONENTIALS AND ITS INVERSE
A logarithmic function is the inverse of an exponential function
Exponential functions have the following characteristics:
Domain: {x є R}
Range: {y > 0}

3. First we must learn how to read logarithmic form:
Standard 11
Writing Exponential form to Logarithmic form
First we must learn how to read logarithmic form:
The expression is read as “log of base b of y”
Examples:

4. Introduction to Logarithmic Functions
FINDING THE INVERSE OF AN EXPONENTIAL x y y x
log = a
Inverse of the Exponential Function
Logarithmic Form
Exponential Function

5. 102 = 100 Log10100 = 2 Logarithms Base Number Index Power Exponent
“10 raised to the power 2 gives 100”
“The power to which the base 10 must be raised to give 100 is 2”
“The logarithm to the base 10 of 100 is 2”
Log10100 = 2

6. 102 = 100 Log10100 = 2 y = bx Logby = x Logarithms 23 = 8 Log28 = 3
is the inverse of
y = bx
Base
Number
102 = 100
Base
Logarithm
23 = 8
Log28 = 3
34 = 81
Log381 = 4
Log525 =2
52 = 25
Log93 = 1/2
91/2 = 3
Log10100 = 2
Number

7. Exponential Form Logarithmic Form
Standard 11
Rewriting Logarithmic Equations
Exponential Form Logarithmic Form

8. 103 = 1000
log = 3
24 = 16
log216 = 4
104 = 10,000
log = 4
32 = 9
log39 = 2
42 = 16
log416 = 2
10-2 = 0.01
log = -2
log464 = 3
43 = 64
log327 = 3
33 = 27
log366 = 1/2
361/2 = 6
log121= 0
120 = 1
p = q2
logqp = 2
xy = 2
logx2 = y
pq = r
logpr = q
logxy = z
xz = y
loga5 = b
ab = 5
logpq = r
pr = q
c = logab
b = ac

9. 103 = 1000
log = 3
24 = 16
log216 = 4
104 = 10,000
log = 4
32 = 9
log39 = 2
42 = 16
log416 = 2
10-2 = 0.01
log = -2
log464 = 3
43 = 64
log327 = 3
33 = 27
log366 = 1/2
361/2 = 6
log121= 0
120 = 1
p = q2
logqp = 2
xy = 2
logx2 = y
pq = r
logpr = q
logxy = z
xz = y
loga5 = b
ab = 5
logpq = r
pr = q
c = logab
b = ac

10. 103 = 1000
log = 3
24 = 16
log216 = 4
104 = 10,000
log = 4
32 = 9
log39 = 2
42 = 16
log416 = 2
10-2 = 0.01
log = -2
log464 = 3
43 = 64
log327 = 3
33 = 27
log366 = 1/2
361/2 = 6
log121= 0
120 = 1
p = q2
logqp = 2
xy = 2
logx2 = y
pq = r
logpr = q
logxy = z
xz = y
loga5 = b
ab = 5
logpq = r
pr = q
c = logab
b = ac

11. 103 = 1000
log = 3
24 = 16
log216 = 4
104 = 10,000
log = 4
32 = 9
log39 = 2
42 = 16
log416 = 2
10-2 = 0.01
log = -2
log464 = 3
43 = 64
log327 = 3
33 = 27
log366 = 1/2
361/2 = 6
log121= 0
120 = 1
p = q2
logqp = 2
xy = 2
logx2 = y
pq = r
logpr = q
logxy = z
xz = y
loga5 = b
ab = 5
logpq = r
pr = q
c = logab
b = ac

12. 103 = 1000
log = 3
24 = 16
log216 = 4
104 = 10,000
log = 4
32 = 9
log39 = 2
42 = 16
log416 = 2
10-2 = 0.01
log = -2
log464 = 3
43 = 64
log327 = 3
33 = 27
log366 = 1/2
361/2 = 6
log121= 0
120 = 1
p = q2
logqp = 2
xy = 2
logx2 = y
pq = r
logpr = q
logxy = z
xz = y
loga5 = b
ab = 5
logpq = r
pr = q
c = logab
b = ac

13. Introduction to Logarithmic Functions
CHANGING FORMS
Example 1) Write the following into logarithmic form:
a) 33 = 27
b) 45 = 256
c) 27 = 128
d) (1/3)x=27
ANSWERS

14. Introduction to Logarithmic Functions
CHANGING FORMS
Example 1) Write the following into logarithmic form:
a) 33 = 27
log327=3
b) 45 = 256
log4256=5
c) 27 = 128
log2128=7
d) (1/3)x=27
log1/327=x

15. Logarithmic Form Exponential Form Solution
Standard 11
Simplifying Logarithmic Equations
Logarithmic Form Exponential Form Solution

16. Introduction to Logarithmic Functions
CHANGING FORMS
Example 2) Write the following into exponential form:
a) log264=6
b) log255=1/2
c) log81=0
d) log1/31/9=2
ANSWERS

17. Introduction to Logarithmic Functions
CHANGING FORMS
Example 2) Write the following into exponential form:
a) log264=6
2^6=64
b) log255=1/2
25^1/2=5
c) log81=0
8^0=1
d) log1/31/9=2
1/3^2=1/9

18. Introduction to Logarithmic Functions
BASE 10 LOGS
Scientific calculators can perform logarithmic operations. Your calculator has a LOG button.
This button represents logarithms in BASE 10 or log10
Example 4) Use your calculator to find the value of each of the following:
a) log101000
b) log 50
c) log -1000
= Out of Domain
= 3
= 1.699