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Logarithmic Base Converter Online


Logarithmic Base Converter | Change of Base Calculator

Logarithmic Base Converter

Convert values between log10, log2, and loge effortlessly

Formula: log2(x) = log10(x) × (log(10) / log(2))
Value in Base 2
6.6439

Understanding Logarithmic Base Conversion

In mathematics and signal processing, we often need to switch between different logarithmic scales. The most common conversion is between Base 10 (Decades) and Base 2 (Octaves).

The Change of Base Formula

To convert a known logarithm in base a to a new base b, we use the following relationship:

logb(x) = loga(x) · logb(a)
or more commonly
logb(x) = loga(x) / loga(b)

Common Conversion Constants

If you are working with filters or frequency response, these shortcuts are highly useful:

  • From Base 10 to Base 2: Multiply by approx 3.3219
  • From Base 2 to Base 10: Multiply by approx 0.3010
  • From Natural Log (ln) to Base 10: Multiply by approx 0.4343

Real-World Application: Audio & RF

In electronics, a decade represents a ten-fold increase in frequency, while an octave represents a two-fold increase. When a filter slope is described as "20dB per decade," you can convert this to octaves using the simulator above to see it is equivalent to approximately "6.02dB per octave."

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