College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.3 - Page 477: 44



Work Step by Step

We know that $ln(x)$ is a natural logarithm with an understood base of $e$. Therefore, $ln(x)+ln(3)=log_{e}x+log_{e}3$. 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, $log_{e}x+log_{e}3=log_{e}(x\times3)=log_{e}3x=ln(3x)$.
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