How do you condense #Ln 3 − 2 ln(8 + 4) #?

1 Answer
Jake M.
Aug 1, 2018

#-ln(48)#

Explanation:

We have to remember two different log rules:
Rule 1: #alogb = log(b^a) #
Rule 2: #log(a) + log(b) = log(ab)#
(Note: Rule 1 is actually a specific case of Rule 2 if #a=b# and you do it a bunch of times)

From that, we can simplify the original:
#ln(3) - 2ln(8+4) #
#ln(3) - 2ln(12) # (by addition)
#ln(3) + ln(12^(-2)) # (by rule 1)
#ln(3 * 12^(-2)) # (by rule 2)
#ln(3/144) # (by definition)
#ln(1/48) = - ln(48) #
our final answer.

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