Question

How do you solve `Log (x+5) - log (x-1) = log (x+2) - log (x-3)`?

Answer 1

`x=13`

Explanation:

To do this problem, you must know that `log(a)+log(b)=log(ab)` and that `log(a)-log(b)=log(a/b)`.

`log(x+5)-log(x-1)=log(x+2)-log(x-3)`

`log(x+5)+log(x-3)-log(x-1)-log(x+2)=0`

`log(((x+5)(x-3))/((x-1)(x+2)))=0`

Remember that `log(a)` is another way of writing `log_10(a)`.

`10^(log(((x+5)(x-3))/((x-1)(x+2))))=10^0`

`((x+5)(x-3))/((x-1)(x+2))=1`

`(x+5)(x-3)=(x-1)(x+2)`

`x^2+2x-15=x^2+x-2`

`2x-15=x-2`

`x=13`