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

Dabae
Jun 28, 2015

#2**+11 **

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

CPhill
Jun 28, 2015

#1**+11 **

2^{x} = 2^{20} - 2^{19}

*Another way of reading this is:*

2^{x} = 2^{20} - 2^{20-1}

Which equates to:

2^{x} = 2^{20} - (2^{20} / 2)

*Now, we get the situation of "x - (x/2) = (x/2)". This means 2 ^{x} is a half of 2^{20}, which is another way of saying:*

2^{x} = 2^{19}

**x = 19**

Sir-Emo-Chappington
Jun 28, 2015

#2**+11 **

Best Answer

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

CPhill
Jun 28, 2015