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Change of base

The base of a logarithm can be changed with

 


Explanation

From the definition of the logarithm follows

aN = x      ⇒      N = loga x

The calculation for base b gives

so that

 


Example 1

You can see that log3 9 = 2, because

but you better calculate this as the logarithm of a powerfunction

 


Example 2

You can see that log3 5 = 1,.465, because

 


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