# 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 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.

# Tags and links to this website

Tags:

logarithm_base_change · logarithm_base_converter · natural_to_decimal_logarithm · decimal_to_natural_logarithm

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# Permalink

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