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Possible Duplicate:
Intuitive use of logarithms

My math teacher "taught" us about logarithms today, but he didn't give any useful information. He just that one is supposed to "add" them to create a quadratic equation. He then gave us this example;

$ \log_4 (x + 4) + \log_4 (x - 4) $

He then told us to solve it. This is how he did it.

$\log_4 (x + 4) + \log_4 (x - 4)$

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

$x = -4, 4$

This does not make a bit of sense to me. What are logarithms for? What do they do? And, most importantly, how would I actually solve this equation?

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    I know that all of you say it is$not$right at all, bit this is _exactly_ what he wrote. That is why I am confused. Thanks for all of the help and links!2011-05-10

1 Answers 1

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If you want to solve $\log_4{(x-4)} + \log_4{(x+4)} = 0$ you combine that to $\log_4{(x-4)(x+4)} = 0$ then exponentiate each side by taking $4^{\log_4{(x-4)(x+4)}} = 4^0$ which gives $ (x-4)(x+4) = 1 $ which you can solve using whichever algebraic method you prefer.

You should get $x = -\sqrt{17}, +\sqrt{17}$, but as I noted in my above comment, the negative solution is extraneous.

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    @user3123: thanks, I noticed that after I posted and have fixed it, after frustratingly losing my internet connection in the middle of the edit :p2011-05-10