## College Algebra (6th Edition)

$ln(7x)$
We know that $ln(x)$ is a natural logarithm with an understood base of $e$. Therefore, $ln(x)+ln(7)=log_{e}x+log_{e}7$. 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, $log_{e}x+log_{e}7=log_{e}(x\times7)=log_{e}7x=ln(7x)$.