Calculating $3^{m-n}=?$ $$9^m + 9^n = 52$$
$$9^m -4 = 2 \cdot 9^n$$
$$3^{m-n}=?$$
Let me show what I've tried

Simpifyling the both equalities. 

$$3^{2^m} + 3^{2n} = 2 \cdot 13 \tag{1}$$
$$3^{2m} -2^2 = 2 \cdot 3^{2n} \tag{2}$$

Diving the second equality by $2$ and we have

$$\frac{3^{2m} -2^2}{2} =3^{2n} \tag{3}$$
Here is where I'm stuck. 
My Kindest Regards!

$$9^m + 9^n = 52$$
$$9^m -4 = 2 \cdot 9^n$$
By substituion, we have
$$(52-9^n)-4=2\cdot 9^n$$
$$48-9^n = 2 \cdot 9^n$$
$$9^n = 16$$
$$3^n=4$$
Substitute $9^n$ inside the first equation and do the same trick to complete the task.
