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

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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
+78643
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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
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#1
+423
+11

2x = 220 - 219

Another way of reading this is:

2x = 220 - 220-1

Which equates to:

2x = 220 - (220 / 2)

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

2x = 219

x = 19

Sir-Emo-Chappington  Jun 28, 2015
#2
+78643
+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

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