# Chapter 9 - Section 9.5 - Common and Natural Logarithms - 9.5 Exercises: 14

3.1112

#### Work Step by Step

We know that logarithms to base 10 are common logarithms, and $log_{10}x$ is equivalent to $log(x)$. Therefore, $log(10^{3.1112})=log_{10}10^{3.1112}$. We know that for all positive numbers $a$ (where $a\ne1$), and all positive numbers $x$, $y=log_{a}x$ means the same as $x=a^{y}$. Therefore, $log_{10}10^{3.1112}=3.1112$, because $10^{3.1112}=10^{3.1112}$.

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