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Expand Logarithms Calculator — result sheet
Expand a logarithm of powered factors into a weighted sum of same-base logarithms and evaluate both forms.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: log_b(x₁^e₁x₂^e₂x₃^e₃)=e₁log_b(x₁)+e₂log_b(x₂)+e₃log_b(x₃).
The calculator shows the product argument and the expanded weighted sum so visitors can verify the product, quotient, and power rules together.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Logarithm base — minimum 1.0E-6; maximum 1000000
- Factor 1 — minimum 1.0E-6; maximum 1000000000
- Exponent 1 — minimum -100; maximum 100
- Factor 2 — minimum 1.0E-6; maximum 1000000000
- Exponent 2 — minimum -100; maximum 100
- Factor 3 — minimum 1.0E-6; maximum 1000000000
- Exponent 3 — minimum -100; maximum 100
Worked example
| Input | Value |
|---|---|
| Logarithm base | 10 |
| Factor 1 | 4 |
| Exponent 1 | 2 |
| Factor 2 | 5 |
| Exponent 2 | 1 |
| Factor 3 | 3 |
| Exponent 3 | -1 |
Product argument = 4²×5/3 ≈ 26.667; both forms evaluate to log₁₀(26.667) ≈ 1.4265.
Assumptions and limits
- The base is positive and not one; factors are positive.
- All terms use the same logarithm base.
- Negative exponents represent reciprocal factors and are retained in the numeric evaluation.
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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