If log3 (12n-1) - log3 (2n+7) = 2 find the value of n.

log3 (12n-1) - log3 (2x+7) =
2

First we will find the
domain.

==> 12n-1 > 0 ==> n>
1/12

==> 2n+7 > 0 ==> n >
-7/2

Then The domain is n > 1/12
.............(1)

Now we will
solve.

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

==> log3 (12n-1)/(2n+7) =
2

Now we will rewrite using exponent
form.

==> (12n-1)/(2n+7) =
3^2

==> (12n-1)/(2n+7) =
9

Now we will multiply by
(2n+7)

==> 12n-1 =
9(2n+7)

==> 12n -1 = 18n +
63

==> -6n =
64

==> n= -64/6 =
-10.6

But -10.6 does not belong to the
domain.

Then the equation has no real
solution.