Logarithm Calculator
A logarithm asks what power of the base gives the number: log₂ 64 = 6, because 2⁶ = 64.
Use 10 for common log; 2.718281828 for ln.
6
- ln x (natural log)
- 4.158883083
- log₁₀ x (common log)
- 1.806179974
- Check
- 2^6 = 64
Step-by-step solution
- log_b(x) = ln x ÷ ln b (change of base)
- = 4.158883083 ÷ 0.6931471806
- = 6
Logarithm Formula
log_b(x) = ln x ÷ ln b
b^(log_b x) = x; bˣ = y ⇔ x = log_b y
Worked Example
log base 2 of 64:
- log_b(x) = ln x ÷ ln b (change of base)
- = 4.158883083 ÷ 0.6931471806
- = 6
log₁₀ x (common log): 1.806179974 · Check: 2^6 = 64
Test-day tip
Logarithms appear on the ACT in Functions questions. Rewrite log_b(x) = y as bʸ = x when the numbers are simple powers, e.g. log₃ 81 = 4.
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Example: The arithmetic sequence 3, 7, 11, …: a10 = 39.
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Permutation and Combination Calculator
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Frequently asked questions
What are the log rules?
log(xy) = log x + log y, log(x/y) = log x − log y and log(xⁿ) = n·log x, in any base.
How do I solve 3ˣ = 20?
Take logs of both sides: x = log 20 ÷ log 3 ≈ 2.727.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Logarithm Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/logarithm-calculator/
IEEE
Scientific Converters, "Logarithm Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/logarithm-calculator/