Logarithm history and transformation

1. Ma’am Anna Carmela Lavin

2. Logarithm

3. JOHN NAPIER
 He coined the word
LOGARITHM
 Logos- Greek word
which means
“Ratio”
 Arithmos- Greek
word which means
“Number”
 Invented during the
advent of Industrial
Revolution

4. Definition of Logarithm
A quantity representing the power to which
a fixed number (the base) must be raised to
produce a given number
𝒙 = 𝒍𝒐𝒈 𝒂 𝒚
Read:
2 = 𝑙𝑜𝑔3 9
4 = 𝑙𝑜𝑔2 16
2 = 𝑙𝑜𝑔7 49

5. Definition of Logarithm
• In general: 𝒚 = 𝒂 𝒙 is equivalent to
𝒙 = 𝒍𝒐𝒈 𝒂 𝒚
• It is the inverse of exponential function
Example
2 𝑥 = 4
3 𝑥 = 27
11 𝑥 = 1331
2 𝑥 = 3

6. Transformation from Exponential
form to Logarithmic Form
Example
1. 𝟒 𝟐
= 𝟏𝟔
2. 𝟔 𝟑
= 𝟐𝟏𝟔
3. 𝟑 𝒚
= 𝟓
4. 𝟐 𝒙
= 𝒚 + 𝟏
5. 𝟏𝟎−𝟑
= 𝟎. 𝟎𝟎𝟏

7. Transformation from Logarithmic
form to Exponential Form
Example
1. 𝑙𝑜𝑔3 81 = 4
2. 𝑙𝑜𝑔2 𝑥 = −5
3. 𝑙𝑜𝑔2
1
64
= −6
4. 𝑙𝑜𝑔10 5 = 0.69897
5. 𝑙𝑜𝑔2
1
32
= −5

8. Finding the value of “x” using
Logarithm
Example
1. 𝑙𝑜𝑔9 x =
1
2
2. 𝑙𝑜𝑔2 x =
2
3
3. 𝑙𝑜𝑔6 x = 4

9. Finding the value of “x” using
Logarithm
Example
1. 𝑙𝑜𝑔2 8 = x
2. 𝑙𝑜𝑔16
1
4
= x
3. 𝑙𝑜𝑔25 125 = x

10. Finding the value of “x” using
Logarithm
Example
1. 𝑙𝑜𝑔 𝒙 4 =
1
2
2. 𝑙𝑜𝑔 𝒙 32 =
5
2
3. 𝑙𝑜𝑔 𝒙 1000 = 3

11. SEATWORK #1
I. Transform the following into Logarithmic
Form (Rx2)
1. 𝑥2 = 𝑦
2. 53 = 125
3. 𝑥21
= 𝑦 − 1
II. Transform the following into Exponential
Form (Rx2)
1. 𝑙𝑜𝑔39 = 2
2. 0.01 = −2
3. 𝑙𝑜𝑔 𝑏
1
𝑥2 = 81