How do you solve log_2 (x+1) - log_2 (x-1) = 4?

1 Answer
Alan P.
Dec 27, 2015

x=17/15

Explanation:

log_2(x+1)-log_2(x-1) = log_2((x+1)/(x-1))

2^4 = 16 rArr 4=log_2(16)

Therefore
color(white)("XXX")log_2(x+1)-log_2(x-1)=4
is equivalent to
color(white)("XXX")log_2((x+1)/(x-1))=log_2(16)

color(white)("XXX")(x+1)/(x-1) = 16

color(white)("XXX")x+1 = 16x-16

color(white)("XXX")-15x = -17

color(white)("XXX")x=17/15

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