Question

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

Answer 1

`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)`