We'll write the equation
log
(x+7) - log 3x = log 5
We could use the quotient property
of the logarithms:
log a - log b = log
(a/b)
We'll put a = x+7 and b = 3x and we'll
get:
log [(x+7)/3x] = log
5
Since the bases are matching, we'll use the one to one
property:
(x+7)/3x = 5
We'll
cross multiply:
x+7 =
15x
We'll isolate x to the left side. For this reason,
we'll subtract 15 both sides:
-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.
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