Question

Q. How to use log table to calculate the value of log? Explain with an example.

Answer 1

1

Choose the correct table. To find loga(n), you'll need a loga table. Most log tables are for base-10 logarithms, called "common logs."Example: log10(31.62) requires a base-10 table.

2

Find the correct cell. Look for the cell value at the following intersections, ignoring all decimal places:Row labeled with first two digits of nColumn header with third digit of nExample: log10(31.62) → row 31, column 6 → cell value 0.4997.

3

Use smaller chart for precise numbers. Some tables have a smaller set of columns on the right side of the chart. Use these to adjust answer if n has four or more significant digits:Stay in same rowFind small column header with fourth digit of nAdd this to previous valueExample: log10(31.62) → row 31, small column 2 → cell value 2 → 4997 + 2 = 4999.

4

Prefix a decimal point. The log table only tells you the portion of your answer after the decimal point. This is called the "mantissa."Example: Solution so far is ?.4999

5

Find the integer portion. Also called the "characteristic". By trial and error, find integer value of p such that a^{p}<nand a^{{p+1}}>n.Example: 10^{1}=10<31.62 and 10^{2}=100>31.62. The "characteristic" is 1. The final answer is 1.4999Note how easy this is for base-10 logs. Just count the digits left of the decimal and subtract one.