Logarithm Calculator
Calculate log base b of any value. Supports any positive base except 1.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Enter a base and a value, and the logarithm is calculated instantly. Results update as you type.
- Enter the base. Common choices are 10 (common log), 2 (binary log), or 2.71828 (natural log). Any positive number except 1 works.
- Enter the value. This must be a positive number. The calculator finds what power you raise the base to in order to get this value.
- Read the result. The answer appears with full precision. Copy or share the result using the buttons provided.
About Logarithms
A logarithm answers the question: "What exponent do I need?" If log base 10 of 100 equals 2, that means 10^2 = 100. Logarithms are the inverse of exponentiation. They appear everywhere in science, engineering, computer science, and finance.
The three most common bases are 10 (common log, used in decibels and pH), e or 2.71828 (natural log, used in calculus and growth modeling), and 2 (binary log, used in computer science). This calculator uses the change-of-base formula: log_b(x) = ln(x) / ln(b).
Frequently Asked Questions
What is a natural logarithm?
A natural logarithm (ln) uses the mathematical constant e (approximately 2.71828) as its base. To calculate ln(x), enter 2.71828 as the base in this calculator.
Why can't the base be 1?
Because 1 raised to any power is always 1, log base 1 is undefined. There is no exponent that makes 1^n equal anything other than 1.
Why must the value be positive?
In real number math, you cannot raise a positive base to any real power and get a negative number or zero. Therefore, log(0) and log of negative numbers are undefined in the real number system.