What is x if log(3x+5)-log(5-x)=log 2?

First, we'll impose the necessary conditions of existence
of logarithms:

3x+5>0 => 3x>-5
=> x >
-5/3

and

5-x>0
=> x<5

The common interval of admissible
values is (-5/3 ; 5).

We'll use the quotient property of
logarithms:

log (3x+5)/(5-x)  = log
2

Since the bases are matching, we'll apply one to one
property:

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

We'll multiply by (5-x) both
sides:

3x + 5 = 10 - 2x

We'll
add 2x both sides:

5x = 5

x =
1

Since the value 1 belongs to the interval
of admissible values for x, the equation has the solution x =
1.