Change of base of a logarithm

\log_a b=\dfrac{\log_c b}{\log_c a}

Result unit: — (liczba)

What it describes

Lets you convert a logarithm to any other base

c

a, b, c

bases and numbers (

>0

a,c\neq 1

)

Lets you compute a logarithm of any base using logarithms of a convenient base (e.g. 10 or

e

— from a calculator).

Computing logarithms with “inconvenient” bases on a calculator.

Express

\log_2 5

in terms of common (base-10) logarithms.

Substitutionauxiliary base

c=10

Result

\log_2 5=\dfrac{\log 5}{\log 2}\approx2.32

Found this formula useful? Share it.

It's free — send it to a friend who's revising.

Teaching? Embed this formula on your site.

Free widget — paste it on your school site, blog or notes. It links to the full version.