how to use log books?
Answers
Step-by-step explanation:
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."[2]
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:[3]
Row labeled with first two digits of n
Column header with third digit of n
Example: 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 row
Find small column header with fourth digit of n
Add this to previous value
Example: 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."[4]
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 {\displaystyle a^{p}<n}a^{p}<n and {\displaystyle a^{p+1}>n}a^{{p+1}}>n.
Example: {\displaystyle 10^{1}=10<31.62}10^{1}=10<31.62 and {\displaystyle 10^{2}=100>31.62}10^{2}=100>31.62. The "characteristic" is 1. The final answer is 1.4999
Note how easy this is for base-10 logs. Just count the digits left of the decimal and subtract one