Math calculator
Logarithm Calculator for Bases
Calculate logarithms for any positive value and base, plus natural log and base-10 log.
Formulalog_b(x) = ln(x) / ln(b)
Formula
Change of base
log_b(x) = ln(x) / ln(b)
log base 10 of 1,000 equals 3.
FAQ6 common questions for this calculator.
FAQs
Can the base be 1?+
No. A logarithm base must be positive and cannot be 1.
What is natural log?+
Natural log uses base e and is often written as ln(x).
How does the Logarithm Calculator calculate the result?+
For the Logarithm Calculator, it uses the Change of base: log_b(x) = ln(x) / ln(b). log base 10 of 1,000 equals 3.
What information do I need to use the Logarithm Calculator?+
For the Logarithm Calculator, enter the known quantities requested by the calculator and use the units implied by the Change of base. If a value is unknown, choose a calculator that solves for that specific variable.
How accurate is the Logarithm Calculator?+
Logarithm Calculator is mathematically reliable for the entered values and selected operation. It follows the Change of base. Rounding, order of operations, and undefined cases can still affect interpretation.
What should I check before using the Logarithm Calculator result?+
For the Logarithm Calculator, check the input values, operation order, rounding precision, and undefined cases before using the result. Compare one changed value at a time when testing scenarios.
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Math guide
How to use the Logarithm Calculator
Calculate logarithms for any positive value and base, plus natural log and base-10 log. The page also explains the change of base and shows a practical example: log base 10 of 1,000 equals 3.
- 1
Enter your details
Enter the values for the logarithm calculator scenario you want to check.
- 2
Check the calculation
Review the result alongside the change of base: log_b(x) = ln(x) / ln(b).
- 3
Compare scenarios
Change one or more inputs to see how they affect the logarithm Calculator result before you use the estimate.