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

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Answer 1 · 2016-06-27T21:13:41

#ln[1/48]#

Simplify the bracket:

#ln3 - 2lncolor(blue)((9+3)) = ln3 - 2lncolor(blue)((12))#

If you are subtracting the logs, you must have been dividing the numbers.

Use the power rule first:

#ln3 - color(red)2ln(12) = ln3 - ln(12)^color(red)2#

Write as a log of a single number:

#=ln[3/(12)^2]#

#= ln(3/144) = ln[1/48]#