Solving \log _2(x-4) + \log _2(x+2) = 4 Here is how I

eszkortwxp

eszkortwxp

Answered question

2022-04-20

Solving
log2(x4)+log2(x+2)=4
Here is how I have worked it out so far:
log2(x4)+log(x+2)=4
log2((x4)(x+2))=4
(x4)(x+2)=24
(x4)(x+2)=16
How do I proceed from here?
x2+2x8=16
x2+2x=24
x(x+2)=24 Which I know is not the right answer
x2+2x24=0 Can't factor this

Answer & Explanation

Elliot Roy

Elliot Roy

Beginner2022-04-21Added 14 answers

It is x22x8=16 my friend. So you get x22x24=0 which factors as (x6)(x+4)=0. Hence, x=6 or x=4.
Kendal Kelley

Kendal Kelley

Beginner2022-04-22Added 16 answers

After (x4)(x+2)=16, you get x22x24=0 (the coefficient of x is 2 not 2). So x=2±1002 by the quadratic formula. So x=6 or x=4

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