How do you condense #ln 3 − 2 ln(9 + 3) #?

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Answer 1 · 2016-09-20T11:41:46

=#ln(3/12^2) = ln(1/48)#

"If you are subtracting logs, then you are dividing the numbers"

#ln 3 - 2ln(9+3)#

=#ln3 - ln(9+3)^2" "larr# using the power law of logs

=#ln(3/(9+3)^2)#

=#ln(3/12^2)" "larr# 2 log terms have become one log term

We can now simplify further:

=#ln(3/144)#

=#ln(1/48)#