Logarithms II — O/L Mathematics

What must I remember about Logarithms II?

• Common logarithms use base 10 (denoted log₁₀ x or simply lg x).
• A common logarithm consists of two components: the Characteristic (integral part, positive, zero, or negative) and the Mantissa (decimal part, always non-negative, obtained from 4-figure tables).
• Characteristic rule: For N ≥ 1, characteristic = (number of digits before decimal point - 1); for 0 < N < 1, characteristic = bar n, where n is the position of the first non-zero digit after decimal point.
• Using antilogarithm tables: The antilog table takes the mantissa to determine the digits of the answer, and the characteristic determines decimal point placement.
• Logarithmic calculation protocol: Apply log laws to convert complex multiplication and division into addition and subtraction of logarithms.

Test yourself (1 minute)

1. Bar notation representation

   A negative characteristic is written with a bar over it (e.g., 2̄.4532 = -2 + 0.4532 = -1.5468); never write -2.4532 because mantissa MUST remain positive.

2. Subtracting logs with bar numbers

   When subtracting a bar number, remember that subtracting a negative becomes an addition: 1.2 - 2̄.5 = 1.2 - (-2 + 0.5) = 1.2 + 2 - 0.5 = 2.7.

3. Four-figure table mean differences

   Add mean difference values to the main table reading; never subtract mean differences.

Practise Logarithms II questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 10, Unit 19)

What should I study first?

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Where does Logarithms II fit in the syllabus?

Grade 10 · Term 2