## Log Table

A log table (logarithm table) is used to accomplish larger computations (such as multiplication, division, squares, and roots) without the assistance of a calculator. A number’s logarithm to a specific base is the exponent by which that base should be raised to yield the original number.

If log216 = x, then 2x = 16 and x = 4

satisfy this equation. So log₂ 16 Equals 4.

If we assume log2 15 = x, we get 2x = 15,

and we can’t get x manually here.

The log table assists us in determining the value of log2 15.

## What is Log Table?

A log table for a certain base is a table of logarithms used to calculate the logarithm of a specific integer to that base. There are different log tables for different bases, such as 10, e (Euler’s number), 2, and so on. The logarithm table is the simplest technique to exactly calculate the value of a number’s log. The logarithmic function is the inverse of the exponential function. In the following part, we will look at the log table for common logarithms.

## Logarithm Table of Common Logarithms

The logarithm with base 10 is known as a common logarithm, and it may be represented as log10 (or) simply log.

The typical log table is shown below (i.e., for base 10). That is, it can return the value of log x (also expressed as log10 x) for any x.

The log table mostly has three sorts of columns:

The first column is referred to as the “primary column,” and it contains numbers ranging from 10 to 99. (all 2 digit numbers).

The second set of columns is referred to as the “differences column,” and it displays the “differences” for the digits 0 to 9.

The “mean differences column” is the third set of columns, and it displays the mean differences from 1 to 9.

Aside from this table, we have log tables for base e (also known as the natural logarithm table) and base 2. (This is referred to as the binary logarithm table).

## Important Notes on Log Table

• If the number of digits following the first non-zero digit is fewer than or equal to 4, a log table can be used to calculate its logarithm. If there are more than four digits, we simply ignore the digits after the fifth.
• The logarithm is the sum of two parts: the characteristic and the mantissa of a number.
• Positive or bad characteristics might exist.
• Mantissa should constantly be upbeat.
• If we need to determine the logarithm of a base other than 10, we may apply the change of base rule logb a = (log a) / (log b), followed by the same table of common logs.