What is it?
The Logarithm Calculator finds the logarithm of a Number in any Base, plus the Natural log ln.
Who is it for?
Class 11–12 and college students, scientists, and anyone solving growth or decay problems.
How to use it
- Enter the Number and the Base.
- Read the logarithm and natural log.
The answer appears as you type; there is no Calculate button. Tap Copy result to copy it, or Share on WhatsApp to send it.
What a logarithm means
log₂(8) = 3 because 2³ = 8. A logarithm answers “what power gives this number?”.
Which base?
- log (base 10): pH, decibels, Richter scale, and many school problems.
- ln (base e ≈ 2.718): calculus, continuous growth and decay.
- log₂: computing (bits).
Solving “how long?” problems
How many years to double money at 8%? Solve 1.08ⁿ = 2: n = log(2) ÷ log(1.08) ≈ 9 years. Any base works, as long as you use the same one on top and bottom.
Errors
Logs are only defined for positive numbers, and the base must be positive and not 1. log(0) and log of a negative number have no answer.
Worked example
log₁₀(1000) = 3; ln(20) ≈ 3.00; log₂(1024) = 10. An earthquake of magnitude 6 has 10 times the wave size of a magnitude 5 because the Richter scale is a base-10 logarithm.
Errors and how to fix them
- “The number must be more than 0”
- “The base must be more than 0 and not 1”
Open the tool: Logarithm Calculator
Still stuck?
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Questions, or an error not listed here?
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