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Solve ?256?^x=?64?^(2-x)

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Ye Hong K. | Experienced Singapore senior high school lecturerExperienced Singapore senior high school...
5.0 5.0 (1 lesson ratings) (1)
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Alternatively,
 
Note that 256 = 28 and 64 = 26.
 
So we could simplify 256^x=64^(2-x) to
(28)x = (26)2-x
28x = 212-6x
8x = 12 - 6x
x = 12/14
x = 6/7
 
Jason S. | My goal is the success of my students. Knowledge-Patience-HonestyMy goal is the success of my students. K...
4.9 4.9 (115 lesson ratings) (115)
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256x = 642-x

Take log4 of both sides:

log4 256x = log4 642-x


x (log4 256) = (2-x) (log4 64)

x (4) = (2-x)(3)

4x = 6 - 3x
 
7x = 6
 
x = 6/7