Logarithm Calculator
Calculate common logarithms, natural logarithms, base-2 logarithms or logarithms with any valid custom base. The result is also displayed as an equivalent exponential relationship so the connection between logarithms and exponents is clear.
How to use the Logarithm Calculator
- Enter a positive number.
- Enter the logarithm base or choose a preset such as base 10, e or base 2.
- The calculator uses the change-of-base relationship ln(x) divided by ln(base).
- Review the logarithm result.
- Compare it with the equivalent exponential statement: base raised to the result equals the original number.
Examples
log base 10 of 1000
log₁₀(1000) = 3 because 10³ = 1000.
log base 2 of 32
log₂(32) = 5 because 2⁵ = 32.
Natural logarithm
The natural logarithm uses the mathematical constant e as its base and is written ln(x).
Frequently asked questions
What is a logarithm?
A logarithm answers the question: what exponent must the base be raised to in order to produce a given number?
What is the natural logarithm?
The natural logarithm, written ln, uses e as its base, where e is approximately 2.71828.
Can a logarithm have base 1?
No. A real logarithm base must be positive and cannot equal 1.
Can I take the real logarithm of zero or a negative number?
Not in the real-number system. Real logarithms require a positive argument.
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