How to Calculate Log
What is Log?
A logarithm is the inverse of exponentiation. log_b(x) answers "to what power must b be raised to get x?" Common logarithm (base 10) is used in science; natural logarithm (base e) in calculus; binary logarithm (base 2) in computer science.
Step-by-Step Guide
- 1log_b(x) = n means b^n = x
- 2Common log: log₁₀(1000) = 3 because 10³ = 1000
- 3Natural log: ln(e) = 1 because e^1 = e
- 4Change of base: log_b(x) = log(x) / log(b)
Worked Examples
Input
log₁₀(10,000)
Result
4
10⁴ = 10,000
Input
log₂(256)
Result
8
2⁸ = 256
Input
ln(20.09)
Result
≈ 3
e³ ≈ 20.09
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