If $2^{20} - 2^{19} = 2^x$, what is the value of $x$?

Vey nice, Sir-Emo-Chappington   ......here's another way to do this

2^20 - 2^19  =  2^x       factor the left side........

2^19 (2 - 1)  = 2^x

2^19 (1)  = 2^x

2^19  = 2^x      .....and it's obvious that x = 19

2^x = 2²⁰ - 2¹⁹

Another way of reading this is:

2^x = 2²⁰ - 2^20-1

Which equates to:

2^x = 2²⁰ - (2²⁰ / 2)

Now, we get the situation of "x - (x/2) = (x/2)". This means 2^x is a half of 2²⁰, which is another way of saying:

2^x = 2¹⁹

x = 19