How do you condense #2log_3x-3log_3y+log_3 8#?

1 Answer
Aug 24, 2016

Answer:

#log_3((8x^2)/y^3)#

Explanation:

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

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

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

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

#rArr2log_3 x=log_3 x^2" and " 3log_3 y=log_3 y^3#

#rArrlog_3 x^2+log_3 8=log_3(8x^2)#

and #log_3(8x^2)-log_3y^3=log_3((8x^2)/y^3)#