Question

How do you solve `log_7 9-log_7(-3x)=2`?

Answer 1

`x=-3/49`

Explanation:

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

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

`color(red)(|bar(ul(color(white)(a/a)color(black)(log_b x=nhArrx=b^n)color(white)(a/a)|))) ........ (B)`

Using (A): `log_7 9-log_7(-3x)=log_7(9/(-3x))`

`=log_7(3/(-x))`

Using (B) : `log_7(3/(-x))=2`

`rArr3/(-x)=7^2=49`

`rArr-49x=3rArrx=-3/49`