Logarithm Calculator
Enter a number and choose the base to compute its logarithm. Supports common log (base 10), natural log (base e) and any custom base you enter.
Logarithm Calculator
Compute log in any base
log_b(x) = ln(x) ÷ ln(b). The logarithm answers: 'to what power must b be raised to get x?'
What Is a Logarithm?
A logarithm answers the question: 'to what power must the base be raised to equal this number?'
If b^y = x, then log_b(x) = y.
**Common bases**: - **Base 10 (common log)**: log(x), used in science and engineering - **Base e (natural log)**: ln(x), ≈ 2.718, used in calculus and finance - **Base 2 (binary log)**: used in computer science
**Change of base formula**: log_b(x) = ln(x) ÷ ln(b) — this lets you compute any base using natural logs.
- log_b(x) = y means b^y = x
- log(1) = 0 for any base
- log(b) = 1 for any base
- Only positive numbers have real logarithms
Worked Example
Example: log_10(1000)
- 10^3 = 1000 - So log_10(1000) = 3
Example: log_2(32) - 2^5 = 32 - So log_2(32) = 5
Example: log_e(7.389) ≈ ln(7.389) - e^2 ≈ 7.389 - So ln(7.389) ≈ 2
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Open calculator →Frequently Asked Questions
Why can't I take the log of 0 or a negative number?
No positive base raised to any power equals 0 or a negative number, so real logarithms are only defined for positive arguments.
What's the difference between log and ln?
log usually means base 10; ln means base e (≈2.718). They differ by a constant factor: ln(x) = log(x) × ln(10) ≈ 2.303 × log(x).
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