SOLUTION: can you help me solving this equation: solve for x log base 2 (2x)= 4- log base 2 (x+2)

Question 756287: can you help me solving this equation: solve for x
log base 2 (2x)= 4- log base 2 (x+2)
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
log base 2 (2x)= 4- log base 2 (x+2)
log base 2 (2x) + log base2 (x + 2) = 4
2x(x + 2) = 2^4
2x^2 + 4x = 16
2x^2 + 4x - 16 = 0
(2x - 4)(x + 4)= 0
Therefore either;
2x - 4 = 0
2x = 4
x = 2
Or
x + 4 = 0
x = -4 (No answer)
Proof:
log base 2 (2 x 2) + log base 2 (2 + 2) = 4
log base 2 (4) + log base 2 (4) = 4
log base 2 (2^2) + log base 2 (2^2) = 4
2 log base 2 (2) + 2 log base 2 (2) = 4
As log base a (a) where a is any integer = 1
Therefore 2 + 2 = 4
Hope this helps
:-)
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