+0

Logarithms

0
98
1

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
Sort:

#1
+18712
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

16 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details