Question 826046: Solve log2(x-2) + log2(x+5) = 1
I thought that I could just cancel the log2 from each, but then I got confused.
Found 2 solutions by Fermat, josmiceli:
Answer by Fermat(136)   (Show Source):
You can put this solution on YOUR website! The log2 bit means that the logs are taken to the base 2!
I normally write this down as log_2
In other words, if we have log_2(x) = p, which means that the log of x, taken to the base 2, is equal to p, then that is just another way of saying,
x = 2^p.
So now we have log_2(x-2) + log_2(x+5) = 1
The thing about logs is that you can add them together, in fact they were, more less, designed for that to happen!
Adding together the logs, we get
log_2{(x-2)(x+5)} = 1
And the law of logs (one of them) tells us that
(x-2)(x+5) = 2^1 = 2
expanding the brackets,
x^2 + 3x - 10 = 2
x^2 + 3x - 12 = 0
Using the quadratic formula, 
So, the two solutions are:  ,  ,
Answer by josmiceli(19441)  (Show Source):
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