log 3x + log 5 = log (x+7)

We could subtract log 5 both
sides:

log 3x = log (x+7) - log
5

We could use the quotient property of the
logarithms:

log 3x = log
[(x+7)/5]

We'll use the one to one
property:

3x = (x+7)/5

We'll
cross multiply:

15x =
x+7

We'll isolate x to the left
side:

14x = 7

We'll divide by
14 both sides:

x = 7/14

x =
1/2

Since the value of x is positive, the solution of the
equation is admissible and it is x = 1/2.