How do you expand #log_3 (d/12)#?

1 Answer
Oct 27, 2017

See explanation.

Explanation:

First we can write the #log# of a quotient as the difference of #log#'s:

#log_3(d/12)=log_3d-log_3 12#

Now if we do the prime decomposition of #12# we can write:

#log_3d-log_3 12=log_3d-log_3 3*4=log_3 d -(log_3 3 +log_3 4)#
#=log_3 d - 1 - log_3 4=log_3 (d/4)-1#