How do you condense #3log_3x+4log_3y-4log_3z#?

1 Answer
Jim G.
Dec 29, 2016

#log_3((x^3y^4)/(z^4))#

Explanation:

Using the #color(blue)"laws of logarithms"#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(logx^nhArrnlogx)color(white)(2/2)|)))#

#rArr3log_3x+4log_3y-4log_3z#

#=log_3x^3+log_3y^4-log_3z^4#

#color(red)(bar(ul(|color(white)(2/2)color(black)(logx+logy=log(xy), logx-logy=log(x/y))color(white)(2/2)|)))#

#rArrlog_3x^3+log_3y^4=log_3(x^3y^4)#

#rArrlog_3(x^3y^4)-log_3z^4=log_3((x^3y^4)/(z^4))#

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