How do you solve $log (x + 3) - log (x - 3) = 2$ $log(x+3)-log(x-3)=2$ ?

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Answer 1 · 2015-10-31T11:06:54

$x = \frac{101}{33}$ $x=101/33$

Use the identity $log (a) - log (b) = log (\frac{a}{b})$ $log(a)-log(b)=log(a/b)$ .

$log (x + 3) - log (x - 3) = 2$ $log(x+3)-log(x-3)=2$

$log (\frac{x + 3}{x - 3}) = 2$ $log(frac{x+3}{x-3})=2$

$\frac{x + 3}{x - 3} = 10^{2} = 100$ $frac{x+3}{x-3}=10^2=100$

$x + 3 = 100 (x - 3) = 100 x - 300$ $x+3=100(x-3)=100x-300$

$303 = 99 x$ $303=99x$

$x = \frac{303}{99} = \frac{101}{33}$ $x=303/99=101/33$

How do you solve log(x+3)−log(x−3)=2log(x+3)-log(x-3)=2?