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# how do i change the base of log?

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how do i change the base of log?

Guest Feb 23, 2017

#1
+19495
+20

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:
$$\qquad {\displaystyle b=x^{\frac {1}{\log _{b}(x)}}.}$$

heureka  Feb 23, 2017
#1
+19495
+20

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:
$$\qquad {\displaystyle b=x^{\frac {1}{\log _{b}(x)}}.}$$

heureka  Feb 23, 2017