Using logarithm tables

Multiplying, dividing and finding roots with log tables.

Indices & Logarithms · O/L Maths

Level 1: The characteristic

Find the whole-number part of a logarithm

The logarithm of any number has two parts: a whole part (the characteristic) and a decimal part (the mantissa).

Numbers ≥ 1: (digits before the point) − 1. Numbers < 1: negative, −(zeros after the point + 1), written with a bar like 2̄.

• log 4567
• 4 digits before the point
• characteristic = 4 − 1 = 3

Level 2: Reading the decimal part

Read a log table and find antilogs

The table gives only the decimal part. Ignore the decimal point, use the digits, and find the whole part separately.

Antilog: find the digits from the decimal part, then place the decimal point using the whole part.

• log 45.23
• Whole part: 2 digits before the point → 1
• Table: row 45, column 2 → 0.6551
• Mean difference (3): +3 → 0.6554
• log 45.23 = 1.6554

Level 3: Multiplying and dividing with logs

Add or subtract logs, then take the antilog

log (a × b) = log a + log b log (a ÷ b) = log a − log b

Steps: 1) find the logs. 2) add or subtract. 3) take the antilog.

• 23.4 × 5.62
• log 23.4 = 1.3692 log 5.62 = 0.7497
• 1.3692 + 0.7497 = 2.1189
• Antilog: decimal part 0.1189 → 1315; whole part 2 → 3 digits before the point
• 23.4 × 5.62 ≈ 131.5

Level 4: Powers and roots

Find powers and roots using logs

log (aⁿ) = n log a log (ⁿ√a) = (log a) ÷ n

For a power, multiply the log by the index; for a root, divide by the root; then take the antilog.

• 2.5³
• log 2.5 = 0.3979
• 3 × 0.3979 = 1.1937
• Antilog: 1.1937 → 15.62