## Intermediate Algebra for College Students (7th Edition)

$\log{10^7} = 7$
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 $\log{10^7}=x$ Use the rule above, with $y=10^7$, to obtain: $10^x=10^7$ Use the rule "If $a^x=a^y$, then $x=y$" to obtain: $x=7$ Therefore, $\log{10^7} = 7$