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# Q) Asked by tirumalasandeep 14th April 2017, 2:30 PM
Dear tirumalasandeep@yahoo.com

Thanks for asking us a question in Ask the Expert section of TopperLearning.com.

We cannot entertain more than 4 questions in a single query per day. In case of multiple questions within a query, please post each question individually and let us know where you are getting stuck so that we would be able to explain things better.

1. Logarithm:

If a is a positive real number, other than 1 and am = x, then we write:
m = logax and we say that the value of log x to the base a is m.

Examples:

(i). 103 1000      log10 1000 = 3.

(ii). 34 = 81      log3 81 = 4.

 (iii). 2-3 = 1 log2 1 = -3. 8 8

(iv). (.1)2 = .01      log(.1) .01 = 2.

1. Properties of Logarithms:

1. loga (xy) = loga x + loga y

 2. loga x = loga x - loga y y

3. logx x = 1

4. loga 1 = 0

5. loga (xn) = n(loga x)

 6. loga x = 1 logx a

 7. loga x = logb x = log x . logb a log a
1. Common Logarithms:

Logarithms to the base 10 are known as common logarithms.

1. The logarithm of a number contains two parts, namely 'characteristic' and 'mantissa'.

Characteristic: The internal part of the logarithm of a number is called its characteristic.

Case I: When the number is greater than 1.

In this case, the characteristic is one less than the number of digits in the left of the decimal point in the given number.

Case II: When the number is less than 1.

In this case, the characteristic is one more than the number of zeros between the decimal point and the first significant digit of the number and it is negative.

Instead of -1, -2 etc. we write 1 (one bar), 2 (two bar), etc.

Examples:-

 Number Characteristic Number Characteristic 654.24 2 0.6453 1 26.649 1 0.06134 2 8.3547 0 0.00123 3

Mantissa:

The decimal part of the logarithm of a number is known is its mantissa. For mantissa, we look through log table.

Regards

Topperlearning Team.
Answered by Expert 15th April 2017, 2:30 PM
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