Answer
2
Work Step by Step
$Evaluate$ $the$ $expression$ $without$ $using$ $a$ $calculator:$
$\log \log 10^{100}$
$$\log \log_{10} 10^{100}$$
Use the Third Property of Logarithms: $\log_a a^x = x$
$$\log \log_{10} 10^{100} = \log 100$$
$$\log_{10} 100$$
Rewrite 100 as $10^2$
$$\log_{10} 10^2$$
Use the Third Property of Logarithms: $\log_a a^x = x$
$$\log_{10} 10^2 = 2$$