<s>[INST] Solve $\log_9(x-4) - \log_9(x-8)= \frac{1}2$ 
Solve $\log_9(x-4) - \log_9(x-8)= \frac{1}2$

$(x-4) - (x-8)= 9^\frac{1}2$
$(x-4) - (x-8)= 3$
The answer is 10 but I am not sure how that was obtained.
 [/INST] $\log_9(x-4)-\log_9(x-8)=\log_9(\frac{x-4}{x-8})=\frac{1}{2}$
$\frac{x-4}{x-8}=9^{1/2}=3$
$x-4 = 3(x-8)=3x-24$
$x-4=3x-24$
$2x=20$
$x=10$
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