# Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.3: 6

$4+log_{10}x$

#### 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 $N\gt0$). We know that $log(x)$ is a common logarithm with an understand base of 10. Therefore, $log(10000x)=log_{10}10000x=log_{10}10000+log_{10}x$. 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, $log_{10}10000=4$, because $10^{4}=10000$. So, $log_{10}10000+log_{10}x=4+log_{10}x$.

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