What is x if 113^(3x-4)-1/113^(x-12)=0?

First, we'll use the negative power property of
exponentials:

1/113^(x-12) =
113^-(x-12)

Now, we'll re-write the
equation:

113^(3x-4) - 113^-(x-12) =
0

We'll add 113^-(x-12) both
sides:

113^(3x-4) =
113^-(x-12)

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

3x - 4 = -x +
12

We'll isolate x to the left side. For this reason, we'll
add x both sides and we'll add 4 both sides:

3x + x  = 12 +
4

We'll combine like terms
:

4x = 16

We'll divide by
4:

x = 4

The
solution of the equation is x = 4.