How to Calculate the Log?
Each item in a log table is made up of two parts: the characteristic and the mantissa. These components help us find the true value of a logarithm for a given logarithmic value. Any Logarithmic value can be represented as
Log of any number = Characteristic + Mantissa
Let’s discuss these components in much detail.
Characteristic
The logarithm’s integral portion has this property. It shows the location of the decimal point in the resultant logarithmic value for a particular logarithm. In other words, it represents the number’s order of magnitude.
In mathematical terms, if you have a number “N” expressed in scientific notation as “N = M × 10k,” where “M” is a number greater than or equal to 1 and less than 10, and “k” is an integer exponent, then the characteristic is “k.”
Characteristic of the logarithm of a number is determined by its position in scientific notation and can be either positive or negative. If the number is greater than 1, the characteristic is found by counting the digits to the left of the decimal point minus one. If the number is less than 1, the characteristic is calculated by counting the zeros immediately following the decimal point, negating the result, and subtracting one. For example,
- If log(500) = 2.698, then the characteristic is 2.
- If log(1000) = 3.0, then the characteristic is 3.
- If log(0.01) = -2.0, then the characteristic is -2.
- If log x = 14.31 = 1.431 × 101, then the characteristic is 1.
Mantissa
The mantissa is the fractional part of result of any logarithm. When paired with the characteristic, it completes the logarithmic value. It is commonly represented as a decimal with numerous decimal places in the log table. Mantissa is always positive and can be calculated with the help of log table, which we will learn in the article further.
- If log(500) = 2.698, then the mantissa here is 698.
- If log(1000) = 3.0, then the mantissa is 0.
- If log(0.01) = -2.0, then the mantissa is 0.
- If log x = 14.31 = 1.431 × 101, then the mantissa is 431.
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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