How do you solve $log_2x + log_2(x-2) = 3$ ?

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Answer 1 · 2016-04-21T18:35:39

$x=4$

Use Property: $log_b(xy)=log_bx+log_by and log_by=x iff x^b=y$

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

$2^3=x^2-2x$

$8=x^2-2x$

$0=x^2-2x-8$

$0=(x-4)(x+2)$

$x-4=0 or x+2=0$

$x=4 or x=-2$

$x=4$

How do you solve log_2x + log_2(x-2) = 3log_2x + log_2(x-2) = 3?