Log Table Elements
In mathematics, the logarithm table is essential for calculating the values of logarithmic functions. The easiest way to determine the value of a specific logarithmic function is by using the log table. This section provides a detailed definition of the logarithmic function and explains how to effectively use the logarithm table.
Understanding Logarithm Tables
Historically, a logarithm table consists of lists of mantissas, which are the decimal parts of exponents that relate to base 10 numbers. For example, the logarithm (the exponent) that applies to the base number 10 to yield 120 is 2.07918.
What is a Logarithm Table?
The logarithmic function is defined as an inverse function to exponentiation. It is expressed as follows:
For x, a > 0, and a ≠ 1,
y = logax, if x = ay
Thus, the logarithmic function can be written as:
f(x) = logax
The most frequently used bases in logarithmic functions are base e and base 10. The log function with base 10 is known as the common logarithmic function, denoted by log10 or simply log.
f(x) = log10
Meanwhile, the log function based on e is referred to as the natural logarithmic function, denoted as loge.
f(x) = logex
To calculate the logarithm of a number, it is beneficial to use the logarithm table instead of relying solely on manual calculations. Before you find the logarithm of a number, it’s important to understand the characteristic part and the mantissa part of that number:
- Characteristic Part – The whole number part of a logarithmic value is the characteristic part. The characteristic of any number greater than one is positive and equals one less than the number of digits to the left of the decimal point. For numbers less than one, the characteristic is negative and one more than the count of zeros to the right of the decimal point.
- Mantissa Part – The decimal part of the logarithmic value is referred to as the mantissa part, which must always be a positive value. If the mantissa is negative, remember to convert it to a positive value.
Logarithm Table – Log Table
Download the Log Table Elements in PDF format using the link given below.