Question

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

Answer 1

`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)`