Solve for "a" if log (2a-3) - 2 = log (a+3)

Given the logarithm
equation:

log (2a-3) -2 = log
(a+3)

We need to solve for
"a"

First we will combine similar
terms.

==> log (2a-3) - log (a+3) =
2

Now we will use the logarithm properties to
solve.

We know that log a - log b = log
a/b

==> log (2a-3)/(a+3) =
2

Now we will rewrite into the exponent
form.

==> (2a-3)/(a+3) =
10^2

==> (2a-3)/(a+3) =
100

Now we will multiply by
(a+3)

==> 2a -3 =
100(a+3)

==> 2a -3 = 100a
+300

==> 98a =
-303

==> a = -303/98 =
-3.01

But the values of a is not defined for
log (2a-3) and log 9a+3)

Then, the equation
has no solution.