Question

How do you solve `log_ 2 (x+2) - log_2 (x-5) = 3`?

Answer 1

same base so you can add the log terms
log2 `(x+2)/(x-5` =3
so now you can convert this to exponent form:
We will have
`(x+2)/(x-5)=2^3`
or

`(x+2)/(x-5)=8` which is pretty simple to solve since

x + 2 = 8(x - 5)
7x = 42
x = 6

quick check by substitution to the original equation will confirm solution.