# Chapter 9 - Section 9.3 - Logarithmic Functions - Exercise Set - Page 700: 53

$\log{100} = 2$

#### Work Step by Step

The given expression involves a common logarithm, meaning that no base is written in, so its base is 10. RECALL: $\log{y}=x \longrightarrow 10^x=y$ Let $\log{100}=x$ Use the rule above, with $y=100$, to obtain: $10^x=100 \\10^x=10^2$ Use the rule "If $a^x=a^y$, then $x=y$" to obtain: $x=2$ Therefore, $\log{100} = 2$

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