Logarithm table and its formulas

📌 Logarithm Table (Base 10) from 0 to 15

x log(x)
1 0.0000
2 0.3010
3 0.4771
4 0.6021
5 0.6990
6 0.7782
7 0.8451
8 0.9031
9 0.9542
10 1.0000
11 1.0414
12 1.0792
13 1.1139
14 1.1461
15 1.1761

📌 Important Logarithm Formulas

1️⃣ Logarithm Definition: If ax = b, then loga(b) = x

2️⃣ Change of Base Formula:
loga(b) = logc(b) / logc(a)

3️⃣ Logarithm Properties:

  • log(A × B) = log A + log B (Product Rule)
  • log(A / B) = log A - log B (Quotient Rule)
  • log(An) = n log A (Power Rule)
  • log(1) = 0
  • log(A) = -log(1/A)

📌 Antilogarithm Formula

If log(x) = y, then x = antilog(y)
Example: log(100) = 2, so antilog(2) = 100

📌 Natural Logarithm (ln) and Common Logarithm (log) Relation

  • ln(x) = loge(x) (Natural Log, base 'e')
  • log(x) = log10(x) (Common Log, base 10)
  • ln(x) = 2.3026 × log(x)
  • log(x) = ln(x) / 2.3026

📌 What is 'e'?

'e' is an important mathematical constant, approximately equal to 2.718. It is the base of the natural logarithm (ln).

Keep Practicing! 💡

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