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Quickly calculate natural, binary, and common logarithms with custom precision. Perfect for math students and scientific calculations.
tools.common-logarithm-calculator.formula.title:
y = log_b(x) ⇔ b^y = x
log₍10₎(100)
tools.common-logarithm-calculator.chart.logarithmDesc
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Still calculating logarithms manually? Enter a positive number, select a log base, and get accurate results instantly. A logarithm represents the inverse operation of exponentiation: if b^y = x, then y is the logarithm of x to base b (log_b(x) = y). This tool directly outputs the calculated values for natural logarithms (base e), binary logarithms (base 2), and common logarithms (base 10).
Q: What is the common logarithm of 100?
A: 2.00 (when rounded to two decimal places). The common logarithm log₁₀(100) means that 10 raised to the power of 2 equals 100.
Q: Can I calculate the logarithm of a negative number or zero?
A: No. The definition of a logarithm requires the input value to be a positive real number. Negative numbers and zero have no valid logarithmic results within the realm of real numbers.
The input value must be a positive real number, otherwise the result will be invalid. The decimal place setting affects rounding precision. Batch calculations require multiple operations, as file uploads are not currently supported.
In algorithm analysis, log₂(n) is frequently used to evaluate time complexity (such as in binary search). Example: Input 256, base 2, output 8 (because 2^8 = 256). We recommend choosing the base according to your specific use case: use ln for scientific computing, log₂ for information theory, and log₁₀ for engineering and measurements.
