Change the base of logarithms.Give an example.

Expert Answers
justaguide eNotes educator| Certified Educator

If we have a logarithm with base m, to change it to logarithm with base n we have to do the following.

log(m) x = [log(n) x] / [ log(n) x]

The process only involves division of the new logarithm by the log of the old base.

giorgiana1976 | Student

We can remember and use the followings: the logarithm in the new base, of the number is the logarithm in the old base, of the number, multiplied by the logarithm in the new base, of the old base.

For instance, we have the log 4 16 and we'll have to change the base 4 into the base 2:

log 2 16 = log 4 16*log 2 4

log 2 (2^4) = log 4 16* log 2 (2^2)

4 log 2 2 = (log 4 16)*2(log 2 2)

But log 2 2 = 1

4 = 2(log 4 16)

(log 4 16) = 4/2=2

But log 4 16 = log 4 (4^2) = 2, therefore, the action of changing the base is verified.

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