What is the integral part of a logarithm of a number called?

The integral part of a logarithm of a number is called the characteristic.

The characteristic is the integer part of the logarithm, while the decimal part is called the mantissa.

For example, the logarithm of 100 to the base 10 is 2. This can be written as:

log₁₀(100) = 2

Here, the characteristic is 2, and the mantissa is 0.

The characteristic is useful in determining the number of digits in the integer part of a number. For example, the characteristic of log₁₀(1000) is 3, which indicates that the number 1000 has four digits (including the leading zero).

The characteristic can be found by subtracting 1 from the number of digits in the integer part of the number. For example, the number 1234 has four digits, so the characteristic of log₁₀(1234) is 3.

The mantissa is a constant value for a given number, regardless of the base of the logarithm. This is because the mantissa represents the fractional part of the logarithm, which is independent of the base.

The characteristic and mantissa are important concepts in logarithmic calculations, especially when working with logarithms of large numbers.