Which answer is extraneous? Why is it extraneous

Question

log 2 (the 2 is in the bottom)x+log2( the two is in the bottom)(x-2)=3

Answer 1

No answers were provided.

 

log₂ x + log₂ (x -2) = 3

 

log₂ x(x - 2) = 3

 

x(x - 2) = 2³ = 8

 

Solving,

 

x² - 2x - 8 = 0

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

x = 4 or x = -2

 

The solution -2 is extraneous, since when you insert it into the original equation, both logarithms are undefined (you cannot find the logarithm of a negative number).