How can you solve this equation 2^x-2^{x-1}=4?

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Hi!,

2^x-2^{x-1}=4

I lose the x if i use my 'normal method of immediately 4=2^2 and bringing everything down.

x-(x-1)=2

Guest Sep 8, 2017

frasinscotland · Answer 1 · 2017-09-08T06:47:55

$2^{x}-2^{x-1} =4$ now factor out to get

$2^{x-1} (2^{1}- 1)=4$

$2^{x-1}(1) =4$

$2^{x-1}=4$ since we know that $2^{2}=4$

then x-1 =2 so x =3.

Check 2^3 - 2^2 = 8 - 4 =4