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Log Calculator
Solve custom logarithm formulas simply by providing the mathematical base and target value.
Logarithm Calculator
log
log()
result = log_10(100)
2
10 2.0000 ≈ 100
Common Log (Base 10)
2.0000
Natural Log (Base e)
4.6052
Binary Log (Base 2)
6.6439
Understanding Logarithms
A logarithm determines exactly what exponent is required to raise a base number to reach a target value. The Calculay Logarithm Calculator allows you to instantly compute any custom mathematical base alongside the native Common, Natural, and Binary logs.
How to Read a Logarithm
If you encounter the equation log₁₀(100) = 2, it simply translates to asking: "10 raised to what power equals 100?". Because 10 * 10 = 100, the answer is 2. The formula structure is always: logBase(Value) = Exponent.
Common Logarithmic Bases
- Common Logarithm (log₁₀ or simply log): Uses a base of 10. This is predominantly used in engineering, chemistry (like calculating the pH of a substance), and measuring the Richter scale for earthquakes.
- Natural Logarithm (ln or logₑ): Uses Euler's number (e ≈ 2.718) as its base. Predominantly used in advanced calculus, financial compounding interest equations, and exponential population growth or radioactive decay models.
- Binary Logarithm (log₂): Uses a base of 2. Extremely common in computer science to calculate binary trees, algorithm time-complexity (Big O notation), and information theory arrays.
Mathematical Input Constraints: By definition, logarithmic functions have strict mathematical boundaries. The "base" must always be a positive number strictly greater than zero and cannot equal exactly 1. Additionally, the "target value" must always be greater than zero. You cannot find the logarithm of a negative number using real mathematics.