Answer
$1+log_{7}x$
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, $log_{7}(7x)=log_{7}7+log_{7}x$.
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, $log_{7}7=1$, because $7^{1}=7$. So, $log_{7}7+log_{7}x=1+log_{7}x$.