Question

Solve Equation log (x-9) = 1 - log x

Answer 1

$\log (x-9) = 1 - \log x \\ D:x-9>0 \wedge x>0\\ D: x>9 \wedge x>0\\ D:x>9\\ \log(x-9)+\log x=1\\ \log x(x-9)=1\\ 10^1=x^2-9x\\ x^2-9x-10=0\\ x^2+x-10x-10=0\\ x(x+1)-10(x+1)=0\\ (x-10)(x+1)=0\\ x=10 \vee x=-1\\ -1\not \in D \Rightarrow x=10$