Answer
$0$
Work Step by Step
By definition, $\log_{3}81=x$ means
$x$ is the exponent with which we raise ($3$) to obtain $81.$
$3^{4}=81 \Rightarrow \log_{3}81=4$
So,
$\log_{10}(\log_{4}(\log_{3}81))$=$\log_{10}(\log_{4}(4))$
By definition, $\log_{4}(4)=x$ means
$x$ is the exponent with which we raise ($4$) to obtain $4.$
$4^{1}=4 \Rightarrow \log_{4}4=1$
So,
$\log_{10}(\log_{4}(\log_{3}81))=\log_{10}(\log_{4}(4))=\log_{10}(1)$
By definition, $\log_{10}(1)=x$ means
$x$ is the exponent with which we raise ($10$) to obtain $1.$
$10^{0}=1 \Rightarrow \log_{10}1=0$
So,
$\log_{10}(\log_{4}(\log_{3}81))$
$=\log_{10}(\log_{4}(4))$
$=\log_{10}(1)$
$=0$
