Logarithm Calculator
log_b(x) for any base b > 0, b ≠ 1, x > 0. Common bases shown side-by-side.
Result
log_10(100)
2.00000000
10^2.0000 = 100.
- log₁₀(x)2.000000
- ln(x)4.605170
- log₂(x)6.643856
- Change-of-baselog_10(x) = ln(x) / ln(10)
Step-by-step
- Use change-of-base: log_10(100) = ln(100) / ln(10) = 4.6052 / 2.3026 = 2.00000000.
How to use this calculator
- Enter x and the base.
- Read the log; the breakdown shows base-10, natural, and base-2 logs for reference.
About this calculator
A logarithm answers: "to what power must I raise the base to get x?" log₁₀(100) = 2 because 10² = 100. Common bases: base 10 (log), base e ≈ 2.718 (ln, natural log), base 2 (used in computer science). Change-of-base formula lets you compute log in any base from natural log: log_b(x) = ln(x) / ln(b).
Frequently asked
log base e ≈ 2.71828, written ln(x). Appears throughout calculus and physics because the derivative of ln(x) is 1/x.
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