Logarithm Table (Log10 & Natural Log Values)
A logarithm table is a classic mathematical tool used to quickly find approximate logarithm values without a calculator. Even though modern calculators are widely available, log tables are still useful in math courses, engineering, physics, and science education to understand how logarithms work.
On this page you’ll find:
- A log10 (common logarithm) table
- An ln (natural logarithm) table
- Clear explanations of how to use logarithm tables
- Step-by-step example calculations
- A section for a downloadable PDF version of the table
Logarithm Calculator
Enter a positive number to find its common and natural logarithms.
What Is a Logarithm?
A logarithm is the exponent to which a base must be raised to obtain a given number.
For example:
log10(100) = 2because10² = 100ln(e³) = 3because the baseeraised to the power 3 equals that value
The two most common types of logarithms are:
- Common logarithm:
log(x)orlog10(x)(base 10) - Natural logarithm:
ln(x)orloge(x)(base e)
Log10 Table - Common Logarithms (Base 10)
The following table shows approximate values of the common logarithm log10(x) for integers from 1 to 10.
| Number (x) | log10(x) |
|---|---|
| 1 | 0.0000 |
| 2 | 0.3010 |
| 3 | 0.4771 |
| 4 | 0.6020 |
| 5 | 0.6990 |
| 6 | 0.7781 |
| 7 | 0.8451 |
| 8 | 0.9031 |
| 9 | 0.9542 |
| 10 | 1.0000 |
A full printable version of the common logarithm table is available: download the log10 reference table (PDF) .
Natural Logarithm Table (ln, Base e)
The table below shows approximate values of the natural logarithm ln(x) for integers from 1 to 10.
| Number (x) | ln(x) |
|---|---|
| 1 | 0.0000 |
| 2 | 0.6931 |
| 3 | 1.0986 |
| 4 | 1.3863 |
| 5 | 1.6094 |
| 6 | 1.7918 |
| 7 | 1.9459 |
| 8 | 2.0794 |
| 9 | 2.1972 |
| 10 | 2.3026 |
How to Use a Logarithm Table
Logarithm tables are used to approximate values when a calculator is not available. The basic idea is to express a number as a product of a value listed in the table and a power of 10, then apply logarithm rules.
Example: Find log10(35)
- Write the number as a product:
35 = 3.5 × 10. - Look up the value of
log10(3.5)in the table. Suppose it is approximately0.5441. - Use the property
log10(a × 10) = log10(a) + 1. - Compute:
log10(35) ≈ 0.5441 + 1 = 1.5441.
In general, if a number can be written as a × 10ⁿ, then:
log10(a × 10ⁿ) = log10(a) + n
Example Calculations with Logarithm Tables
Example 1: ln(7)
From the natural log table: ln(7) ≈ 1.9459.
Example 2: log10(250)
- Write the number as a product:
250 = 2.5 × 10². - Look up
log10(2.5)in the table (approximately0.3979). - Use the property:
log10(2.5 × 10²) = log10(2.5) + 2. - Compute:
log10(250) ≈ 0.3979 + 2 = 2.3979.