Indices and Logarithms - II — O/L Mathematics

What must I remember about Indices and Logarithms - II?

• Common Logarithms (Base 10): Logarithm of number N to base 10: log10 N = Characteristic + Mantissa.
• Characteristic (c): Integer part of logarithm: For N ≥ 1, Characteristic = (Number of digits before decimal point - 1); For 0 < N < 1, Characteristic = -(Number of leading zeros + 1), written as bar notation (e.g., c = 2̄ for 0.035).
• Mantissa (m): Non-negative decimal fraction obtained from 4-figure logarithm tables; Mantissa depends SOLELY on the sequence of significant digits, completely independent of decimal point position.
• Logarithmic Laws for Calculations: log(A × B) = log A + log B; log(A / B) = log A - log B; log(Aⁿ) = n × log A; log(ⁿ√A) = (1/n) × log A.

Test yourself (1 minute)

1. Bar characteristic arithmetic

   In 2̄.4560, the characteristic -2 is negative but the mantissa +0.4560 is POSITIVE: 2̄.4560 = -2 + 0.4560 = -1.5440.

2. Dividing a bar characteristic

   To divide 2̄.4560 by 3: Rewrite characteristic as a multiple of 3: 2̄.4560 = (3̄ + 1.4560); then (3̄ + 1.4560) / 3 = 1̄.4853.

3. Anti-logarithm conversion

   Look up the mantissa in the Antilogarithm table to obtain digits, then use the characteristic c to place the decimal point (multiply by 10^c).

Practise Indices and Logarithms - II questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 11, Unit 3)

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Where does Indices and Logarithms - II fit in the syllabus?

Grade 11 · Term 1