Solve the logarithmic equation. Round your answer to two decimal places. $${\log }_{10}(x-9)+{\log }_{10}x=3$$

A) $x=36.44$
B) $x=495.50$
C) $x=-27.44$
D) $x=36.44,x=-27.44$
E) there is no solution

Using the logarithmic property ${\log }_a(b)+{\log }_a(c)={\log }_a(bc)$ , the equation becomes ${\log }_{10}((x-9)x)=3$ . Converting from logarithmic to exponential form gives $(x-9)x=10^3$ , which simplifies to $x^2-9x-1000=0$ . Solving this quadratic equation yields $x=36.44$ as the only valid solution since $x=-27.44$ would result in a negative argument for the logarithm, which is undefined.