Question

the characteristic of 46.263 is​

Answer 1

Answer:

Consider 10^0 = 1. We say log 1 to the base 10 = 0.

Consider 10^1 = 10. We say log 10 to the base 10 = 1

So what about the log of numbers which lie between 1 and 10? i.e., say log 7. It should be between 0 and 1. i.e., 0.______.

Now consider 10^2= 100. Hence we say log 1 to the base 100 = 2

So what about the log of numbers which lie between 10 and 100? Say log 36.9. It should be between 1 and 2.

i.e., 1. ______

Now consider 10^3 = 1000. Hence we say log 1 to the base 1000 = 3

So what about the log of numbers which lie between 100 and 1000? Say log 592.68. It should be between 2 and 3

i.e., 2. ______

So we see that log 7 = 0.______, log 36.9 = 1._______, log 592.68 = 2.________.

Hence we observe numbers with single digit before decimal point have logarithm = 0.______,

numbers with two digits before decimal point have logarithm = 1.______,

numbers with three digits before decimal point have logarithm = 2.______, and so on

Each of the numbers in the logarithm value 0, 1, 2,……….before the decimal point is called as the characteristic of the logarithm of a number.

The decimal part of the logarithm, which we obtain from logarithm tables, is called the mantissa.

So, logarithm of a number consists of two parts: the integral part called the characteristic, the decimal part, the mantissa