Solve for x :

log (x + 3) − log (x − 3) = 1

Given,

$\Rightarrow \log \space (x + 3) − \log \space (x − 3) = 1 \\[1em] \Rightarrow \log \space \dfrac{(x + 3)} {(x − 3)} = \log \space 10 \\[1em] \Rightarrow \dfrac{(x + 3)} {(x − 3)} = 10 \\[1em] \Rightarrow (x + 3) = (x − 3) \times 10 \\[1em] \Rightarrow x + 3 = 10x − 30 \\[1em] \Rightarrow 10x - x = 3 + 30 \\[1em] \Rightarrow 9x = 33 \\[1em] \Rightarrow x = \dfrac{33}{9} \\[1em] \Rightarrow x = \dfrac{11}{3}.$

Hence, the value of x = $\dfrac{11}{3}$.