To solve these equations, we will go through each one step by step:

1. (x-9) = 77
To isolate x, we can add 9 to both sides of the equation:
x = 77 + 9
x = 86

2. 450:9X-19 = 50
First, we need to simplify the left side of the equation:
450 / (9x) - 19 = 50
Divide both sides by 50 to isolate the fraction:
9x/50 - 19/50 = 1
Now, add 19/50 to both sides:
9x/50 = 1 + 19/50
9x/50 = 69/50
To solve for x, multiply both sides by 50/9:
x = (69/50) * (50/9)
x = 69/9
x = 7.67

3. 89 - (73 - x) = 20
First, simplify the parentheses:
89 - 73 + x = 20
Combine like terms:
16 + x = 20
Subtract 16 from both sides:
x = 20 - 16
x = 4

4. 10 + 2x = 4^15;4^13
We can simplify this equation by substituting 4^15 and 4^13 with their respective values:
10 + 2x = 1073741824; 67108864
Now, we have two separate equations:
10 + 2x = 1073741824
10 + 2x = 67108864
To solve for x, subtract 10 from both sides in each equation:
2x = 1073741814; 67108854
Divide both sides by 2:
x = 536870907; 33554427

5. 4x - 20 = 2^5:2^3
First, simplify the right side of the equation:
4x - 20 = 32/8
4x - 20 = 4
Add 20 to both sides:
4x = 24
Divide both sides by 4:
x = 6