Question

How do you solve `log_6(x+8)+log_6 7=2`?

Answer 1

`x=-20/7`

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)|)))........(A)`
Applies to logarithms to any base.

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

From (A) `log_6(x+8)+log_6 7=log_6(7(x+8))`

From (B) `7x+56=6^2=36rArrx=-20/7`