Log Table Elements

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Logarithm Table

In mathematics, the logarithm table is used to find the value of the logarithmic function. The simplest way to find the value of the given logarithmic function is by using the log table. Here the definition of the logarithmic function and procedure to use the logarithm table is given in detail.

Historically, a logarithm table is a list of mantissa (the decimal parts) of the exponents that make base 10 numbers. They mean that the logarithm (the exponent) that acts on the base number 10 to make 120 is 2.07918.

Logarithm Table

The logarithmic function is defined as an inverse function to exponentiation. The logarithmic function is stated as follows

For x, a > 0, and a≠1,

y= log_ax, if x = a^y

Then the logarithmic function is written as:

f(x) = log_ax

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

f(x) = log₁₀

The log function to the base e is called the natural logarithmic function and it is denoted by log_e^.

f(x) = log_e x

To find the logarithm of a number, we can use the logarithm table instead of using a mere calculation. Before finding the logarithm of a number, we should know about the characteristic part and mantissa part of a given number

Characteristic Part – The whole part of a number is called the characteristic part. The characteristic of any number greater than one is positive, and if it is one less than the number of digits to the left of the decimal point in a given number. If the number is less than one, the characteristic is negative and is one more than the number of zeros to the right of the decimal point.
Mantissa Part – The decimal part of the logarithm number is said to be the mantissa part and it should always be a positive value. If the mantissa part is in a negative value, then convert it into a positive value.