How to Read a Logarithm Table Step by Step
A logarithm table helps find the logarithm (base 10) of numbers quickly without a calculator. Follow these steps to understand how to use it effectively.
Step 1: Understand What a Logarithm Is
A logarithm tells the power to which 10 must be raised to get a number.
Example: log10(100) = 2 because 10² = 100.
Step 2: Know What’s in a Logarithm Table
The table lists logarithms (base 10) for numbers between 1 and 10. Each logarithm has two parts:
- Characteristic: The whole number part.
- Mantissa: The decimal part (found in the table).
Example: log(234) = 2.3692 → Characteristic = 2, Mantissa = 0.3692
Step 3: Express the Number in Scientific Form
Write the number as M × 10ⁿ, where M is between 1 and 10.
Example: 234 = 2.34 × 10² → log(234) = log(2.34) + 2
Step 4: Use the Table to Find the Mantissa
- Find the first two digits (row) — for 2.34, use 23.
- Find the third digit (column) — for 2.34, use 4.
- Read the value where the row and column meet — that’s the mantissa.
Example: From the table, log(2.34) = 0.3692
Step 5: Add the Characteristic
Add the power of 10 from Step 3 to the mantissa.
Example: log(234) = 2 + 0.3692 = 2.3692
Step 6: For Numbers Less Than 1
If the number is less than 1, the characteristic is negative, but the mantissa stays positive.
Example: log(0.0234) = log(2.34) − 2 = −1.6308 (written as −2 + 0.3692)
Step 7: For More Accuracy
If the number has more digits (like 2.345), use the mean difference column in the table to adjust the mantissa slightly.
Quick Summary
| Step | Action | Example (234) |
|---|---|---|
| 1 | Write in scientific form | 2.34 × 10² |
| 2 | Find log(2.34) from table | 0.3692 |
| 3 | Add characteristic (2) | 2.3692 |
This method helps find logarithms quickly and accurately using a standard log table.
How to Read a Logarithm Table Step by Step
A logarithm table helps find the logarithm (base 10) of numbers quickly without a calculator. Follow these steps to understand how to use it effectively.
Step 1: Understand What a Logarithm Is
A logarithm tells the power to which 10 must be raised to get a number.
Example: log10(100) = 2 because 10² = 100.
Step 2: Know What’s in a Logarithm Table
The table lists logarithms (base 10) for numbers between 1 and 10. Each logarithm has two parts:
- Characteristic: The whole number part.
- Mantissa: The decimal part (found in the table).
Example: log(234) = 2.3692 → Characteristic = 2, Mantissa = 0.3692
Step 3: Express the Number in Scientific Form
Write the number as M × 10ⁿ, where M is between 1 and 10.
Example: 234 = 2.34 × 10² → log(234) = log(2.34) + 2
Step 4: Use the Table to Find the Mantissa
- Find the first two digits (row) — for 2.34, use 23.
- Find the third digit (column) — for 2.34, use 4.
- Read the value where the row and column meet — that’s the mantissa.
Example: From the table, log(2.34) = 0.3692
Step 5: Add the Characteristic
Add the power of 10 from Step 3 to the mantissa.
Example: log(234) = 2 + 0.3692 = 2.3692
Step 6: For Numbers Less Than 1
If the number is less than 1, the characteristic is negative, but the mantissa stays positive.
Example: log(0.0234) = log(2.34) − 2 = −1.6308 (written as −2 + 0.3692)
Step 7: For More Accuracy
If the number has more digits (like 2.345), use the mean difference column in the table to adjust the mantissa slightly.
Quick Summary
| Step | Action | Example (234) |
|---|---|---|
| 1 | Write in scientific form | 2.34 × 10² |
| 2 | Find log(2.34) from table | 0.3692 |
| 3 | Add characteristic (2) | 2.3692 |
This method helps find logarithms quickly and accurately using a standard log table.