Log Table Solved Examples
Example 1: A log table is used to compute the logarithms of various values. Determine their characteristics and mantissa if log x = -3.4606.
Solution:
We know that a number’s logarithm is the sum of its characteristics and mantissa. However, keep in mind that the mantissa is always positive.
log x = -3.4606
⇒ log x = -3 – 0.4606
However, mantissa cannot be negative. So we add and subtract 1.
log x = (-3 – 1) + (1 – 0.4606)
⇒ log x = -4 + 0.5394
Thus, log x = characteristic + mantissa
As a result, the characteristic is -4 and the mantissa is 0.5394.
Example 2: Determine the value of log10 5.632.
Solution:
To find the common logarithm of the number 5.632 we need to evaluate characteristic and mantissa and add them together.
To find mantissa find the row labeled “56” and the column “3” in the log table.
The intersection of this row and column gives you the mantissa without mean difference: 7505.
And then find the mean difference for the same row and column 2 i.e., 2.
Thus, Mantissa = 7505 + 2 = 7507.
To find the characteristic, since 5.632 is greater than 1, the characteristic is the number of digits to the left of the decimal point minus 1.
In this case, there are two digits to the left of the decimal point, so the characteristic is 0.
Thus, log10 (5.632) = characteristic + mantissa
log10 (5.632) = 0 + 0.7507 = 0.7507.
So, log10 (5.632) ≈ 0.7507.
Example 3: Find the value of log10 0.0751 using log table.
Solution:
To find the common logarithm of the number 0.0751 we need to evaluate characteristic and mantissa and add them together.
To find mantissa find the row labeled “75” and the column “1” in the log table.
The intersection of this row and column gives you the mantissa without mean difference: 8756.
As there is not digit after that, we don’t need to check the mean difference.
Thus, Mantissa is 8756.
To find the characteristic, since 0.0751 is smaller than 1, the characteristic of 7.5 × 10-2 is -2.
Thus, log10 0.0751 = characteristic + mantissa
log10 0.0751 = -2 + 0.8756 = -1.1244
So, log10 0.0751 ≈ -1.1244
Log Table | How to Use Logarithm Table with Examples
Log Table or Logarithmic Table is used to make complex calculations easy. Calculating a logarithm problem without a log table is a very frustrating task.
Let’s learn the method of calculating logs using Logarithm Tables.
Table of Content
- What is a Log Table?
- Log Table 1 to 100
- How to use Log Table
- How to Calculate the Log?
- Logarithmic Table 1 To 10
- Natural Log Table for 1 To 10
- Log and Antilog Table
- FAQs
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