Question

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

Answer 1

`-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.