A comprehensive guide to finding logarithms and antilogarithms for CBSE Class 11 Applied Mathematics, covering characteristics, mantissas, and interpolation.
A logarithm of a number x to a base 10 is expressed as log10(x) = y. It consists of two parts: the Characteristic (the integer part, representing the magnitude) and the Mantissa (the decimal part, which is always positive and found using log tables).
• Step 1: Determine the characteristic. Since 456.7 > 1, the number of digits before the decimal is 3. Characteristic = 3 - 1 = 2.
• Step 2: Look up the mantissa in the log table. Find the row for '45', column '6', which is 6589. Add the mean difference for '7', which is 7.
• Step 3: 6589 + 7 = 6596. Therefore, mantissa is .6596.
Answer: log10(456.7) = 2.6596
Antilogarithm is the inverse process of finding a logarithm. If log x = y, then x = antilog(y). To find the antilog, we focus only on the decimal part (mantissa) in the antilog table and use the characteristic to determine the decimal point position.
• Step 1: Identify the characteristic (2) and the mantissa (.7218).
• Step 2: Look for .72 in the row and 1 in the column of the antilog table, which gives 5260. Add the mean difference for 8, which is 10.
• Step 3: 5260 + 10 = 5270. Since the characteristic is 2, the decimal point is placed after 2+1=3 digits.
• Step 4: The number is 527.0
Answer: antilog(2.7218) = 527.0