Answer
$1+log_{9}x$
Work Step by Step
Based on the product rule of logarithms, we know that $log_{b}(MN)=log_{b}M+log_{b}N$ (for $M\gt0$ and $N\gt0$).
Therefore, $log_{9}(9x)=log_{9}9+log_{9}x$.
Based on the definition of the logarithmic function, we know that $y=log_{b}x$ is equivalent to $b^{y}=x$ (for $x\gt0$ and $b\gt0$, $b\ne1$).
Therefore, $log_{9}9=1$, because $9^{1}=9$. So, $log_{9}9+log_{9}x=1+log_{9}x$.
