The term log is a short form of logarithm in mathematics, which is the inverse operation of exponentiation. Instead of raising a number to a power, a logarithm calculator tells us what power we need to raise a base number to in order to get another number using Log calculator.
Logarithm Calculator
Common Log (log10)
Natural Log (ln)
Custom Base
Result:
The logarithm of a number x to the base b is written as: logb(x).
Types of Logarithms:
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Common Logarithm:
- Written as log(x) with base 10.
- Used in science and engineering.
- Example: log(1000) = 3 because 103 = 1000.
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Natural Logarithm:
- Written as ln(x) with base e (where e ≈ 2.718).
- Common in calculus, finance, and natural growth models.
- Example: ln(e2) = 2.
Basic Logarithm Rules-Log Calculator
| Rule Name | Formula | Example |
|---|---|---|
| Product Rule | logb(xy) = logb(x) + logb(y) | log2(4 × 8) = log2(4) + log2(8) |
| Quotient Rule | logb(x/y) = logb(x) − logb(y) | log3(81/9) = log3(81) − log3(9) |
| Power Rule | logb(xr) = r × logb(x) | log2(82) = 2 × log2(8) |
| Change of Base | logb(x) = logk(x) / logk(b) | log4(16) = log(16) / log(4) |
| Identity Rule | logb(b) = 1 | log10(10) = 1 |
| Log of 1 | logb(1) = 0 | log3(1) = 0 |