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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

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) = 2 because 10² = 100
  • ln(e³) = 3 because the base e raised to the power 3 equals that value

The two most common types of logarithms are:

  • Common logarithm: log(x) or log10(x) (base 10)
  • Natural logarithm: ln(x) or loge(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.

Log10 values for numbers from 1 to 10
Number (x)log10(x)
10.0000
20.3010
30.4771
40.6020
50.6990
60.7781
70.8451
80.9031
90.9542
101.0000

Traditional printed logarithm tables often include values for many more numbers, such as from 1 to 100 or even 1 to 1000. These extended tables provide greater precision for scientific and mathematical calculations.

Natural Logarithm Table (ln, Base e)

The table below shows approximate values of the natural logarithm ln(x) for integers from 1 to 10.

Natural log (ln) values for numbers from 1 to 10
Number (x)ln(x)
10.0000
20.6931
31.0986
41.3863
51.6094
61.7918
71.9459
82.0794
92.1972
102.3026

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)

  1. Write the number as a product: 35 = 3.5 × 10.
  2. Look up the value of log10(3.5) in the table. Suppose it is approximately 0.5441.
  3. Use the property log10(a × 10) = log10(a) + 1.
  4. 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)

  1. Write the number as a product: 250 = 2.5 × 10².
  2. Look up log10(2.5) in the table (approximately 0.3979).
  3. Use the property: log10(2.5 × 10²) = log10(2.5) + 2.
  4. Compute: log10(250) ≈ 0.3979 + 2 = 2.3979.