Logarithm Calculator
Calculate any logarithm — common log (base 10), natural log (ln), binary log (log₂), or any custom base — with the formula shown.
What Does This Tool Do?
Calculate logarithms in any base — log₁₀ (common log), ln (natural log), log₂ (binary log), or any custom base — with the change-of-base formula shown and the antilog (base^result) verified.
Key Features
4 Base Options
log₁₀, ln, log₂ or any custom base.
Change-of-Base
Formula ln(x)/ln(b) shown.
Antilog Check
Verifies result by computing b^answer.
Instant
Immediate result.
How to Use
- Enter the number x.
- Select the base (log₁₀, ln, log₂ or custom).
- Click Calculate to see the logarithm.
Frequently Asked Questions
What is a logarithm?▾
log_b(x) = y means b^y = x. The logarithm answers: "to what power must I raise b to get x?" E.g. log₁₀(100) = 2 because 10² = 100.
What is the natural logarithm (ln)?▾
ln(x) = log_e(x), where e ≈ 2.71828. It is the inverse of e^x and appears throughout calculus, physics and compound growth formulas.
What is the change of base formula?▾
log_b(x) = ln(x) / ln(b). This allows calculating any base using just the natural log, which is what computers compute natively.