Logarithm base converter
Calculator converts given logarithm value from one base (e.g. decimal) to another (e.g. natural) quickly.

Calculations data - source base and value and destination base

Source logarithm
Base of your logarithm, which you're going to change
Value of your logarithm, which you're going to convert
Destination logarithm
Goal base wich, you want to get

Results - your logarithm in new base

Source logarithm
Base of logarithmdecimal logarithm (base 10)
Value of logarithm10
Destination logarithm
Base of logarithmnatural logarithm (e number base)
Value of logarithm2.302585093

Some facts

  • You can change the base of your logarithm by applying general formula:
    logax=logbxlogba\log_{a} x = \dfrac{\log_{b} x}{\log_{b} a}
    • a - the source logarithm base (the one you start with)
    • x - the value of source logarithm (the one you're going to convert)
    • b - final logarithm base (the result)
  • In natural and technical sciences, conversion between decimal logarithm and natural logarithm (→ see e number) is particularly frequent. We can apply above formula to get following expressions:
    lnx=log10xlog10e2.3026log10x\ln x = \dfrac{\log_{10} x}{\log_{10} e} \approx 2.3026 \cdot \log_{10} x
    log10x=lnxln100.4343lnx\log_{10} x = \dfrac{\ln x}{\ln 10} \approx 0.4343 \cdot \ln x
  • If you want to learn more about the logarithmic function and its properties, check our other calculator: Logarithm.

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