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January 30, 2015

January 30, 2015

Posted by **anonymous** on Tuesday, January 8, 2013 at 6:30am.

log2(x+4)-log4x=2

please show work

- math -
**Reiny**, Tuesday, January 8, 2013 at 8:46amwe should have the same base in the logs

let log_{4}x = y

then 4^y = x

2^(2y) = x

log_{2}x = 2y

y = (1/2)log_{2}x

= log_{2}x^(1/2)

= log_{2}√x

then log_{4}x = log_{2}√x

log_{2}[ (x+4)/√x] = 2

(x+4)/√x = 2^2 = 4

x+4 = 4√x

square both sides

x^2 + 8x + 16 = 16x

x^2 - 8x + 16 = 0

(x-4)^2 = 0

x-4 = 0

x = 4

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