Why does lnalnb=ln(ab)?

It does not matter what base we use providing the same base is used for all logarithms, here we are using bease e.

Cerchiamo di definire A,B.C as follows=:

A=lnaa=eA,

B=lnbb=eB

C=ln(ab)ab=eC

From the last definition we have:

ab=eCeC=eAeB

And using the law of indices:

eC=(eA)(eB)=eAB

And as as the exponential is a 1:1 monotonic continuous function, we have:

C=AB

E così:

ln(ab)=lnalnb QED

Lascia un commento