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

1 Answer
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.