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how do i change the base of log?

Guest Feb 23, 2017

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 #1
avatar+18369 
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how do i change the base of log?

 

Change of base

The logarithm \(log_b(x)\) can be computed from the logarithms of \(x\) and \(b\) with respect to an arbitrary base \(k\) using the following formula:
\(\qquad {\displaystyle \log _{b}(x)={\frac {\log _{k}(x)}{\log _{k}(b)}}.\,}\) ,

 

Typical scientific calculators calculate the logarithms to bases 10 and \(e\).
Logarithms with respect to any base b can be determined using either of these two logarithms by the previous formula:
\(\qquad {\displaystyle \log _{b}(x)={\frac {\log _{10}(x)}{\log _{10}(b)}}={\frac {\log _{e}(x)}{\log _{e}(b)}}.\,}\)

 

Given a number \(x\) and its logarithm \(log_b(x)\) to an unknown base \(b\), the base is given by:
\(\qquad {\displaystyle b=x^{\frac {1}{\log _{b}(x)}}.}\)

 

laugh

heureka  Feb 23, 2017
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1+0 Answers

 #1
avatar+18369 
+20
Best Answer

how do i change the base of log?

 

Change of base

The logarithm \(log_b(x)\) can be computed from the logarithms of \(x\) and \(b\) with respect to an arbitrary base \(k\) using the following formula:
\(\qquad {\displaystyle \log _{b}(x)={\frac {\log _{k}(x)}{\log _{k}(b)}}.\,}\) ,

 

Typical scientific calculators calculate the logarithms to bases 10 and \(e\).
Logarithms with respect to any base b can be determined using either of these two logarithms by the previous formula:
\(\qquad {\displaystyle \log _{b}(x)={\frac {\log _{10}(x)}{\log _{10}(b)}}={\frac {\log _{e}(x)}{\log _{e}(b)}}.\,}\)

 

Given a number \(x\) and its logarithm \(log_b(x)\) to an unknown base \(b\), the base is given by:
\(\qquad {\displaystyle b=x^{\frac {1}{\log _{b}(x)}}.}\)

 

laugh

heureka  Feb 23, 2017

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