Log Calculator (Logarithm)

Calculate any of the three values in the logarithm equation logb(x) = y

Calculate any of the three values in the logarithm equation logb(x) = y.

Log Calculator (Logarithm)

Please provide any two values to calculate the third in the logarithm equation logbx = y. It can accept "e" as a base input for natural logarithms.

Logarithm Formula:

logb(x) = y

Where:

  • b = base (must be positive and ≠ 1)
  • x = number (must be positive)
  • y = result (logarithm)

Natural Logarithm: loge(x) = ln(x)

Common Logarithm: log10(x)

Calculate Logarithm

log
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💡 Tip: Leave one field empty to calculate that value. Use "e" for natural logarithm.

About Logarithms

A logarithm is the inverse operation to exponentiation. It answers the question: "To what power must the base be raised to get the number?"

Common Logarithms:

  • Natural Log (ln): loge(x)
  • Common Log: log10(x)
  • Binary Log: log2(x)
  • Custom Base: logb(x)

Logarithm Properties:

  • • logb(1) = 0
  • • logb(b) = 1
  • • logb(xy) = logb(x) + logb(y)
  • • logb(x/y) = logb(x) - logb(y)
  • • logb(xn) = n·logb(x)

Applications:

  • • Scientific calculations
  • • Sound intensity (decibels)
  • • pH scale (acidity)
  • • Richter scale (earthquakes)
  • • Information theory
  • • Algorithm complexity

Common Values:

• ln(e) = 1
• ln(1) = 0
• log10(10) = 1
• log10(100) = 2
• log2(2) = 1
• log2(8) = 3