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.

Tags and links to this website#

What tags this calculator has#


This is permalink. Permalink is the link containing your input data. Just copy it and share your work with friends:

Links to external sites (leaving Calculla?)#

JavaScript failed !
So this is static version of this website.
This website works a lot better in JavaScript enabled browser.
Please enable JavaScript.