Logarithm Calculator

What is the Logarithm Calculator?

Calculate the logarithm of a number in any base, plus natural log and log base 10. Logarithms answer the question “what power gives this number?”, and they appear in pH, decibels, earthquake scales and compound growth.

How to use the Logarithm Calculator

1. Enter your number, your base.
2. Results update automatically as you type; you can also press Calculate.
3. Read the output: log_b(x), natural log ln(x), log₁₀(x), log₂(x).
4. Use the 📊 chart to see the result visually, then copy or share it.

Formula and method

Worked example

With number = 1,000, base = 10, the Logarithm Calculator returns log_b(x): 3; natural log ln(x): 6.90775527898; log₁₀(x): 3.

Where the Logarithm Calculator helps in real life

A chemistry student has a hydrogen ion concentration of 0.0001 mol/L. The base-10 log gives −4, so the pH is 4.

An investor wants to know how many years money takes to triple at 6%. Dividing ln(3) by ln(1.06) gives about 18.9 years.

Common mistakes to avoid

• Taking the log of zero or a negative number.
• Using ln when the formula needs log base 10.
• Forgetting that a change of 1 on a log scale is a tenfold change.
• Rounding intermediate logs too early.

💡 Practical tip: log₁₀(1000) equals 3 because 10³ = 1000 — raise the base to your answer to check any result.

Tips for better results

• Check which base your formula expects.
• Use ln (base e) for continuous growth problems.
• Verify by raising the base to the result.

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