Question

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

Answer 1

`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))`