How to Use Logarithmic Tables
Choose the correct table., Find the correct cell., Use smaller chart for precise numbers., Prefix a decimal point., Find the integer portion.
Step-by-Step Guide
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Step 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. -
Step 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 n Column header with third digit of n Example: log10(31.62) → row 31, column 6 → cell value
0.4997. , 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. , 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 , Also called the "characteristic".
By trial and error, find integer value of p such that ap<n{\displaystyle a^{p}<n} and ap+1>n{\displaystyle a^{p+1}>n}.
Example: 101=10<31.62{\displaystyle 10^{1}=10<31.62} and 102=100>31.62{\displaystyle 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. -
Step 3: Use smaller chart for precise numbers.
-
Step 4: Prefix a decimal point.
-
Step 5: Find the integer portion.
Detailed Guide
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.
Look for the cell value at the following intersections, ignoring all decimal places:
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. , 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. , 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 , Also called the "characteristic".
By trial and error, find integer value of p such that ap<n{\displaystyle a^{p}<n} and ap+1>n{\displaystyle a^{p+1}>n}.
Example: 101=10<31.62{\displaystyle 10^{1}=10<31.62} and 102=100>31.62{\displaystyle 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.
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Jessica Stevens
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