How do you solve log_2 (x+1) - log_2 (x-1) = 4log2(x+1)log2(x1)=4?

1 Answer
Dec 27, 2015

x=17/15x=1715

Explanation:

log_2(x+1)-log_2(x-1) = log_2((x+1)/(x-1))log2(x+1)log2(x1)=log2(x+1x1)

2^4 = 16 rArr 4=log_2(16)24=164=log2(16)

Therefore
color(white)("XXX")log_2(x+1)-log_2(x-1)=4XXXlog2(x+1)log2(x1)=4
is equivalent to
color(white)("XXX")log_2((x+1)/(x-1))=log_2(16)XXXlog2(x+1x1)=log2(16)

color(white)("XXX")(x+1)/(x-1) = 16XXXx+1x1=16

color(white)("XXX")x+1 = 16x-16XXXx+1=16x16

color(white)("XXX")-15x = -17XXX15x=17

color(white)("XXX")x=17/15XXXx=1715