Log Calculator
Compute log base 10, natural log, log base 2 or a logarithm in any custom base. The change-of-base formula is worked through step by step, and a table compares the input’s logarithm across all common bases at once.
TheCalculators — Log Calculator
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log base 10 of 100
2
Check: 10^2 ≈ 100 = x ✓
- x
- 100
- Base
- 10
- log₍10₎(x)
- 2
- log₁₀(x)
- 2
- ln(x)
- 4.60517
- log₂(x)
- 6.643856
- x in E-notation
- 1.0000e+2
Change of base, step by step
- 1Change-of-base formulalog_b(x) = ln(x) ÷ ln(b)
- 2Substitutelog_10(100) = ln(100) ÷ ln(10) = 4.60517 ÷ 2.302585
- 3Divide= 2
- 4Verify10^2 = 100 ≈ x ✓
Logarithms of 100 in every common base
Most useful next
Formula
log_b(x) = ln(x) ÷ ln(b), valid for x > 0, b > 0, b ≠ 1
Pro tips
- • log₂ answers “how many times must I halve/double?” — it is the heart of algorithm complexity (O(log n)).
- • log₁₀ tells you the digit count: log₁₀(x) rounded up is the number of digits in the integer x.
- • ln is the natural log with base e ≈ 2.71828 — it appears everywhere growth is proportional to size.
FAQ
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