Log Table Elements PDF

Log Table Elements - Summary

In mathematics, the logarithm table is crucial for calculating the values of logarithmic functions. One of the easiest ways to find the value of a specific logarithmic function is by using the log table. This section provides a simple definition of the logarithmic function and guides you on 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 instance, 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 the inverse function to exponentiation. It is expressed as follows:

For x, a > 0, and a ≠ 1,

y = log_ax, if x = a^y

Thus, the logarithmic function can be written as:

f(x) = log_ax

The most commonly used bases in logarithmic functions are base e and base 10. The log function with base 10 is called the common logarithmic function, denoted by log₁₀ or simply log.

f(x) = log₁₀

Meanwhile, the log function based on e is known as the natural logarithmic function, denoted as log_e^.

f(x) = log_ex

To find the logarithm of a number, it is very useful to use the logarithm table instead of just relying on manual calculations. Before you look for 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 called 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

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