Logarithm Calculator
Calculate the logarithm of a number to any base, plus the natural log and common log.
Enter a positive number and a base to compute logb(x). For example: log base 10 of 1000 = 3.
What is a Logarithm?
A logarithm answers the question: to what power must a base be raised to produce a given number? If by = x, then logb(x) = y. Logarithms are widely used in science, engineering, and finance.
Common Logarithm Formulas
- Logarithm to base b: logb(x) = ln(x) / ln(b)
- Natural logarithm: ln(x) = loge(x), where e ≈ 2.71828
- Common logarithm: log10(x) = log base 10 of x
Tip: The number x must be greater than 0, and the base b must be greater than 0 and not equal to 1. For example, log base 2 of 8 equals 3, because 2³ = 8.
Related Calculators
Note: This calculator provides mathematical calculations for logarithms based on the formulas described. While we strive for accuracy, please verify important calculations independently. This tool is for educational and informational purposes and should not be the sole basis for financial, academic, or professional decisions.