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Logarithm Change-of-Base Calculator — result sheet
Calculate a logarithm in any valid base using natural logarithms.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: log_b(x)=ln(x)/ln(b); requested base uses ln(x)/ln(new base).
The result reports both the original-base logarithm and the same argument evaluated in the requested base.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Logarithm argument — minimum 1.0E-6; maximum 1000000000000
- Original base — minimum 1.0E-6; maximum 1000000
- Requested base — minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Logarithm argument | 100 |
| Original base | 10 |
| Requested base | 2 |
log₁₀(100)=2 and log₂(100)≈6.644.
Assumptions and limits
- The argument is positive and each base is positive and not equal to 1.
- The logarithm uses real-number arithmetic.
- Rounding, complex branches, and symbolic simplification are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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