Reading Log Tables: Step-by-step Guide + Practice Quiz

Reading Logarithm Tables

Step-by-step guide with worked examples, a demo table, a quick calculator, and a practice quiz.

Key ideas

• Logarithm: The logarithm of a number \(N\) (base 10) is the power \(x\) such that \(10^x = N\).
• Characteristic: The integer part of the log. It tells you the order of magnitude of the number.
• Mantissa: The decimal part of the log. It is always positive and is read from the log table.
• Mean difference: Used to adjust for the 4th digit of the number for accuracy.

Goal: To find \(\log_{10}(N)\), split into characteristic and mantissa. Read mantissa from the table, then add the characteristic.

Step-by-step: How to read the log table

1. Normalize the number: Write \(N\) in standard form (between 1 and 10) × \(10^k\).
2. Characteristic: The exponent \(k\) is the characteristic.
3. Mantissa: Take the digits of the normalized number (ignoring the power of 10). Use the first 2 digits for the row, the 3rd digit for the column, and the 4th digit for mean difference.
4. Add them: Logarithm = characteristic + mantissa (from table).

Tiny demo log table (for illustration)

Row	Col 0	Col 1	Col 2	Col 3	Col 4	Col 5	Col 6	Col 7	Col 8	Col 9
23	0.3617	0.3625	0.3632	0.3640	0.3648	0.3655	0.3663	0.3670	0.3678	0.3686
24	0.3802	0.3809	0.3817	0.3825	0.3832	0.3840	0.3847	0.3855	0.3862	0.3870

This miniature shows the structure only. Use the official full table in exams.

Worked example

Find: \(\log_{10}(2345)\)

• Write \(2345 = 2.345 \times 10^3\)
• Characteristic = 3
• Mantissa: look up 2345 → row 23, col 4, mean difference for 5
• Table gives ≈ 0.3700
• Final log = 3 + 0.3700 = 3.3700

Instant log calculator (to check your table reading)

Enter N:

Use this only to check your answers. In exams, you must read from the official table.

Practice quiz: Reading log tables

1) The characteristic of \(\log_{10}(2345)\) is:

2 3 4 5

2) The mantissa is always:

Positive Negative Equal to the characteristic Ignored

3) To find \(\log_{10}(N)\), the row in the table is determined by:

The first two digits of N The last two digits of N The characteristic only The mean difference

4) The mean difference in a log table is used to:

Correct for the 4th digit Find the characteristic Normalize the number Ignore extra digits

5) For \(N = 0.02345\), the characteristic of \(\log_{10}(N)\) is:

-1 -2 0 1

Built for students: follow the step-by-step, then verify with the calculator, and finally test yourself with the quiz.