📌 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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