Log Approximation(+/-0.05)
Step 1: If want to approximate the logs, remember this:
|
Range |
Value |
| 1.1 | 25 |
| 1.2 | 15 |
| 1.3 | 11 |
| 1.4 | 09 |
| 1.5-5.5 | 07 |
| 5.6-7.5 | 08 |
| 7.6-9.0 | 09 |
| 9.1-10 | 10 |
*Important- This approximation is about +/- 0.05. For some values you can add 0.05 or subtract 0.05.
Example 1
log (1.5)
Now, we want to take log of 1.5.
look at the table above. You'll see 1.5-5.5 and its value is 07.
Formula for log (x) is
Formula : X/(value) +/- 0.05
So, Here
(1.5/07)= 0.21-0.05=0.16
Actual value is 0.176.
Example 2
log (5.5)
5.5/07
0.79-0.05
0.74
Actual Value:0.74
Example 3
log (8)
8/09
0.88
Actual Value:0.90
Example 4
log (9.3)
9.3/10
0.93+0.05
0.98
Actual value:0.97
Example 5
log (42)
When you get this type of value, you cannot divide 42 by 07.
But you can use some math. (significant figures)
Convert 42 to 4.2*101
log of 101 always equal to 1. Then log (4.2*10) is
1+(4.2/07)
1.60
Actual value:1.62
Example 6
log (56898)
This problem seems harder but It is not.
Convert to two significant figure.
5.7*104
log of 104 is 4 and log of 5.7 is (5.7/08)
4.71+0.05
4.76
Actual value: 4.76
Example 7
log (0.0008756)
Convert to two significant figure.
8.8*10-4
log of 10-4 is -4.and log of 8.8 is (8.8/9)
-4+(0.98-0.05)
-4+(0.93)
-3.07
Actual value:-3.06
Example 8
log (5.3*10-6)
-6+(5.3/07)
-5.24
Actual value:-5.26
Exercise
log (6.8)
log (3569800)
log (0.05897)
log (0.0000092365)
-log (1.2356*10-9)
* Check all answers in your calculator.