Calculadora de Logaritmo
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
log_b(x) = ln(x) / ln(b)
About this calculator
The Logarithm Calculator solves log_b(x) for any positive base not equal to 1. The logarithm is the exponent to which the base must be raised to obtain the argument. For example, log_2(8) = 3 because 2³ = 8. The tool uses the change-of-base formula: log_b(x) = ln(x) / ln(b), where ln is the natural logarithm. Just enter the base and argument; the result is computed instantly with high precision.
When to use? In financial math, to calculate doubling time for investments (compound interest). In sciences, to measure pH (base 10 logarithm) or decibels. In computing, for algorithm complexity analysis (base 2 logarithm). It is useful whenever you need to find exponents in exponential equations.
Cautions: the base must be positive and not equal to 1. The argument must be positive (logarithm of zero or negative does not exist in real numbers). The calculator rounds to 10 decimal places; for critical calculations, verify precision. Remember that log_b(1) = 0 for any valid base.
Frequently asked questions
What is the difference between natural logarithm and common logarithm?
Natural logarithm (ln) has base e (approximately 2.71828). Common logarithm (log) has base 10. The calculator uses ln internally, but the result is equivalent for any base.
Can I calculate the logarithm of a negative number?
No, in real numbers, logarithm of a negative number or zero is not defined. For complex numbers, there are definitions, but this calculator works only with reals.
How do I calculate base 10 logarithm using this calculator?
Simply set the base to 10 and enter the argument. The result will be the decimal logarithm. For example, log_10(100) = 2.
What does log_b(1) = 0 mean?
Any positive base raised to zero equals 1. Therefore, the logarithm of 1 in any base is always zero.
Does the calculator work for fractional bases?
Yes, as long as the base is positive and not equal to 1. For example, log_(0.5)(4) = -2, since (0.5)^(-2) = 4.