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 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

# Some facts

• 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.