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

1 Answer
Jim G.
Aug 29, 2016

#ln(2/3)#

Explanation:

Using the #color(blue)"laws of logarithms".#These laws apply to logs to any base.

#color(orange)"Reminder"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(logx^nhArrnlogx)color(white)(a/a)|)))#

#rArr2ln9=ln9^2=ln81#

#color(red)(|bar(ul(color(white)(a/a)color(black)(logx+logy=log(xy))color(white)(a/a)|)))#

#rArrln3+ln18=ln(3xx18)=ln54#

#color(red)(|bar(ul(color(white)(a/a)color(black)(logx-logy=log(x/y))color(white)(a/a)|)))#

#rArrln54-ln81=ln(54/81)=ln(2/3)#
#color(blue)"------------------------------------------------------"#

#rArrln3-2ln9+ln18=ln(2/3)#

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