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# Logarithms

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When changing the base of a logarithm, from

logb(a) = log(a)/log(b)

Is it possible for the bases of the new logarithms to be any number? or only base 10?

Guest Aug 17, 2017
#1
+19835
0

When changing the base of a logarithm, from

logb(a) = log(a)/log(b)

Is it possible for the bases of the new logarithms to be any number? or only base 10?

You can use any number:

Change of Base Formula

The change of base formula for logarithms is:

$$\begin{array}{|rcll|} \hline \log_a{(x)} &=& \dfrac{ \log_b{(x)} } { \log_b{(a)} } \\ \hline \end{array}$$

Example:

$$\begin{array}{|rcll|} \hline \log_4{(16)} &=& \log_4{(4^2)} \\ &=& 2 \\\\ \log_4{(16)} &=& \frac{ \log_2{(16)} }{ \log_2{(4)} } \\ &=& \frac{ \log_2{(2^4)} }{ \log_2{(2^2)} } \\ &=& \frac{ 4\cdot \log_2{(2)} }{ 2\cdot \log_2{(2)} } \\ &=& \frac{ 4 }{ 2 } \\ &=& 2 \quad \checkmark \\ \hline \end{array}$$

heureka  Aug 17, 2017