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	decimal logarithm (base 10)natural logarithm (e number base)binary logarithm (base 2)other
Value of your logarithm, which you're going to convert
Destination logarithm
Goal base wich, you want to get	decimal logarithm (base 10)natural logarithm (e number base)binary logarithm (base 2)other

Results - your logarithm in new base#

Source logarithm
Base of logarithm	decimal logarithm (base 10)
Value of logarithm	10
Destination logarithm
Base of logarithm	natural logarithm (e number base)
Value of logarithm	2.302585093

You can change the base of your logarithm by applying general formula:

$\log_{a} x = \dfrac{\log_{b} x}{\log_{b} a}$
where:
- 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:

$\ln x = \dfrac{\log_{10} x}{\log_{10} e} \approx 2.3026 \cdot \log_{10} x$

$\log_{10} x = \dfrac{\ln x}{\ln 10} \approx 0.4343 \cdot \ln x$
If you want to learn more about the logarithmic function and its properties, check our other calculator: Logarithm.

Tags:

Tags to Polish version:

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