Question 248665
{{{log(t,(3ab))}}} Start with the given expression



{{{log(t,(3a))+log(t,(b))}}} Break up the log using the identity {{{log(c,(xy))=log(c,(x))+log(c,(y))}}}.


Note: Using the identity, this means that x=3a and y=b



{{{log(t,(3))+log(t,(a))+log(t,(b))}}} Break up the first log using the identity {{{log(c,(xy))=log(c,(x))+log(c,(y))}}} again.


Note: Using the identity, this means that x=3 and y=a



So {{{log(t,(3ab))=log(t,(3))+log(t,(a))+log(t,(b))}}}



------------------------------------------------------------

As you can see (or if you do more examples, you will see), the log of the product of any number of factors is simply the sum of the logs of those factors. In other words, this idea generalizes for any number of terms being multiplied. 


So for example, {{{log(t,(3abcde))=log(t,(3))+log(t,(a))+log(t,(b))+log(t,(c))+log(t,(d))+log(t,(e))}}}