The document shows the step-by-step work of using logarithms to solve the equation 0.87 / (28.9 * 0.785). It begins by writing the equation in logarithmic form and then applies logarithm properties to simplify the expression. The final simplified expression of 2.5837 is then converted back to a decimal value of 0.03834 using antilogarithms.

1. 1) In log Multiply change into Addition
2) In log Divide change into subtraction
3) In log we never find power
4) Characteristics = value – 1
5) log 1 = 0
6) log 10 = 1
LOGARITHM
Key point of logarithm

2. EXERCISE 3.6
Find the value of the following by using logarithms:
3)
𝟎.𝟖𝟕
𝟐𝟖.𝟗 (𝟎.𝟕𝟖𝟓)
Solution:

3. EXERCISE 3.6
Find the value of the following by using logarithms:
3)
𝟎.𝟖𝟕
𝟐𝟖.𝟗 (𝟎.𝟕𝟖𝟓)
Solution:
Log (0.87) – [log (28.9) + log (0.785)]

4. EXERCISE 3.6
Find the value of the following by using logarithms:
3)
𝟎.𝟖𝟕
𝟐𝟖.𝟗 (𝟎.𝟕𝟖𝟓)
Solution:
Log (0.87) – [log (28.9) + log (0.785)]
Log (8.7 x 10-1) – [log (28.90) + log (7.850 x 10-1)

5. EXERCISE 3.6
Find the value of the following by using logarithms:
3)
𝟎.𝟖𝟕
𝟐𝟖.𝟗 (𝟎.𝟕𝟖𝟓)
Solution:
Log (0.87) – [log (28.9) + log (0.785)]
Log (8.7 x 10-1) – [log (28.90) + log (7.850 x 10-1)
Log (8.700) + log (10)-1 – [log (28.90) + Log (7.850) + log (10)-1

7. EXERCISE 3.6
Find the value of the following by using logarithms:
3)
𝟎.𝟖𝟕
𝟐𝟖.𝟗 (𝟎.𝟕𝟖𝟓)
Solution:
Log (0.87) – [log (28.9) + log (0.785)]
Log (8.7 x 10-1) – [log (28.90) + log (7.850 x 10-1)
Log (8.700) + log (10)-1 – [log (28.90) + Log (7.850) + log (10)-1
(0.9395) + (-1)(1) –[1.4609 + 0.8949 + (-1)(1)]

8. EXERCISE 3.6
Find the value of the following by using logarithms:
3)
𝟎.𝟖𝟕
𝟐𝟖.𝟗 (𝟎.𝟕𝟖𝟓)
Solution:
Log (0.87) – [log (28.9) + log (0.785)]
Log (8.7 x 10-1) – [log (28.90) + log (7.850 x 10-1)
Log (8.700) + log (10)-1 – [log (28.90) + Log (7.850) + log (10)-1
(0.9395) + (-1)(1) –[1.4609 + 0.8949 + (-1)(1)]
0.9395 – 1 - [1.4609 + 0.8949 – 1]

9. EXERCISE 3.6
Find the value of the following by using logarithms:
3)
𝟎.𝟖𝟕
𝟐𝟖.𝟗 (𝟎.𝟕𝟖𝟓)
Solution:
Log (0.87) – [log (28.9) + log (0.785)]
Log (8.7 x 10-1) – [log (28.90) + log (7.850 x 10-1)
Log (8.700) + log (10)-1 – [log (28.90) + Log (7.850) + log (10)-1
(0.9395) + (-1)(1) –[1.4609 + 0.8949 + (-1)(1)]
0.9395 – 1 - [1.4609 + 0.8949 – 1]
0.9395 – 1 – 1.3558

10. EXERCISE 3.6
Find the value of the following by using logarithms:
3)
𝟎.𝟖𝟕
𝟐𝟖.𝟗 (𝟎.𝟕𝟖𝟓)
Solution:
Log (0.87) – [log (28.9) + log (0.785)]
Log (8.7 x 10-1) – [log (28.90) + log (7.850 x 10-1)
Log (8.700) + log (10)-1 – [log (28.90) + Log (7.850) + log (10)-1
(0.9395) + (-1)(1) –[1.4609 + 0.8949 + (-1)(1)]
0.9395 – 1 - [1.4609 + 0.8949 – 1]
0.9395 – 1 – 1.3558
- 1.4163

11. EXERCISE 3.6
Find the value of the following by using logarithms:
3)
𝟎.𝟖𝟕
𝟐𝟖.𝟗 (𝟎.𝟕𝟖𝟓)
Solution:
Log (0.87) – [log (28.9) + log (0.785)]
Log (8.7 x 10-1) – [log (28.90) + log (7.850 x 10-1)
Log (8.700) + log (10)-1 – [log (28.90) + Log (7.850) + log (10)-1
(0.9395) + (-1)(1) –[1.4609 + 0.8949 + (-1)(1)]
0.9395 – 1 - [1.4609 + 0.8949 – 1]
0.9395 – 1 – 1.3558
- 1.4163
- 1.4163 + 2 -2

12. EXERCISE 3.6
Find the value of the following by using logarithms:
3)
𝟎.𝟖𝟕
𝟐𝟖.𝟗 (𝟎.𝟕𝟖𝟓)
Solution:
Log (0.87) – [log (28.9) + log (0.785)]
Log (8.7 x 10-1) – [log (28.90) + log (7.850 x 10-1)
Log (8.700) + log (10)-1 – [log (28.90) + Log (7.850) + log (10)-1
(0.9395) + (-1)(1) –[1.4609 + 0.8949 + (-1)(1)]
0.9395 – 1 - [1.4609 + 0.8949 – 1]
0.9395 – 1 – 1.3558
- 1.4163
- 1.4163 + 2 -2
0.5837 – 2
2.5837
For Antilog

14. EXERCISE 3.6
Find the value of the following by using logarithms:
3)
𝟎.𝟖𝟕
𝟐𝟖.𝟗 (𝟎.𝟕𝟖𝟓)
Solution:
Log (0.87) – [log (28.9) + log (0.785)]
Log (8.7 x 10-1) – [log (28.90) + log (7.850 x 10-1)
Log (8.700) + log (10)-1 – [log (28.90) + Log (7.850) + log (10)-1
(0.9395) + (-1)(1) –[1.4609 + 0.8949 + (-1)(1)]
0.9395 – 1 - [1.4609 + 0.8949 – 1]
0.9395 – 1 – 1.3558
- 1.4163
- 1.4163 + 2 -2
0.5837 – 2
2.5837
For Antilog
5837
3828 + 6

15. EXERCISE 3.6
Find the value of the following by using logarithms:
3)
𝟎.𝟖𝟕
𝟐𝟖.𝟗 (𝟎.𝟕𝟖𝟓)
Solution:
Log (0.87) – [log (28.9) + log (0.785)]
Log (8.7 x 10-1) – [log (28.90) + log (7.850 x 10-1)
Log (8.700) + log (10)-1 – [log (28.90) + Log (7.850) + log (10)-1
(0.9395) + (-1)(1) –[1.4609 + 0.8949 + (-1)(1)]
0.9395 – 1 - [1.4609 + 0.8949 – 1]
0.9395 – 1 – 1.3558
- 1.4163
- 1.4163 + 2 -2
0.5837 – 2
2.5837
For Antilog
5837
3828 + 6
3834

16. EXERCISE 3.6
Find the value of the following by using logarithms:
3)
𝟎.𝟖𝟕
𝟐𝟖.𝟗 (𝟎.𝟕𝟖𝟓)
Solution:
Log (0.87) – [log (28.9) + log (0.785)]
Log (8.7 x 10-1) – [log (28.90) + log (7.850 x 10-1)
Log (8.700) + log (10)-1 – [log (28.90) + Log (7.850) + log (10)-1
(0.9395) + (-1)(1) –[1.4609 + 0.8949 + (-1)(1)]
0.9395 – 1 - [1.4609 + 0.8949 – 1]
0.9395 – 1 – 1.3558
- 1.4163
- 1.4163 + 2 -2
0.5837 – 2
2.5837
For Antilog
5837
3828 + 6
3834
0.03834