Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Here is how I have worked it out so far:

$\log _2(x-4)+\log(x+2)=4$

$\log _2((x-4)(x+2)) = 4$

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

$(x-4)(x+2)=16$

How do I proceed from here?

$x^2+2x-8 = 16$

$x^2+2x = 24$

$x(x+2) = 24$ Which I know is not the right answer

$x^2+2x-24 = 0$ Can't factor this

share|improve this question
2  
+1 for showing the working. –  Aryabhata Nov 18 '10 at 0:29
    
Yes it makes it alot easier to help when you show the work like this. –  Unreasonable Sin Nov 18 '10 at 0:55
    
Something like this in mathematica simply checks for error :Solve[Log[2, x - 4] + Log[2, x + 2] == 4, x] –  Quixotic Nov 18 '10 at 9:58

3 Answers 3

up vote 5 down vote accepted

It is $x^2-2x-8 = 16$ my friend. So you get $x^2 - 2x -24 = 0$, which factors as $(x-6)(x+4) = 0$. Hence, $x=6$ or $x = -4$.

share|improve this answer
4  
I suspect that the x=-4 root is meant to be discarded (otherwise your claiming log_2(-8)+log_2(-2)=4). –  Douglas S. Stones Nov 18 '10 at 0:49
1  
@ Douglas S. Stones: which is not totally false since I could take a branch of $\log_2(-8)$ and another branch of $\log_2(-2)$ to get $4$. But yes if you are talking about "conventional" logarithms, I need to discard $x=-4$. –  user17762 Nov 18 '10 at 7:29

After $(x-4)(x+2)=16$, you get $x^2-2x-24=0$ (the coefficient of $x$ is $-2$ not $2$). So $x=\frac{2\pm \sqrt{100}}{2}$ by the quadratic formula. So $x=6$ or $x=-4$

share|improve this answer
    
In the square root, how do you get 100? 4 - (4)(1)(24) = 4 - (96) = 92 –  rcapote Nov 18 '10 at 0:24
    
$4 - (4)(1)(-24)=100$. The constant is $-24$, not $24$ –  Timothy Wagner Nov 18 '10 at 0:27
    
Ah, I get it. Negative numbers are going to be the end of my math career :P –  rcapote Nov 18 '10 at 0:32

The quadratic formula: $$ x = \frac{ -b \pm \sqrt{b^2 - 4 a c} }{2a} = \frac{-2 \pm \sqrt{2^2 - 4 \times 1 \times (-24) }}{2 \times 1} $$ 4 + 96 in the square root.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.