How do you simplify #ln 3 − 2 ln 9 + ln 18 #?

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Answer 1 · 2015-09-01T23:29:31

#ln 3 - 2 ln 9 + ln 18 = ln (2/3) = ln 2 - ln 3#

Use:#color(white)(XX)ln a + ln b = ln (ab)#

and:#color(white)(XX)ln a - ln b = ln (a/b)#

to simplify:

#ln 3 - 2 ln 9 + ln 18#

#=ln 3 + ln 18 - ln 9^2#

#=ln (3*18) - ln 81#

#=ln 54 - ln 81#

#=ln (54/81)#

#=ln (2/3)#

#=ln 2 - ln 3#