How do you solve $log_2(x+5)-log_2(x-2)=3$ ?

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Answer 1 · 2016-07-24T15:08:34

x=3

$log_2(x+5)-log_2(x-2)=3$

combine the log terms as follows

$log_2 ((x+5)/(x-2))=3$

then by definition

$((x+5)/(x-2))=2^3 = 8$

then some algebra

$x+5= 8x-16$

$7x = 21, x=3$

How do you solve log_2(x+5)-log_2(x-2)=3log_2(x+5)-log_2(x-2)=3?