Answer
$1$
Work Step by Step
By definition, $\log_{4}256=x$ means
$x$ is the exponent with which we raise ($4$) to obtain $256.$
$4^{4}=256 \Rightarrow \log_{4}256=4$
So,
$\log_{2}(\log_{2}(\log_{4}256))=\log_{2}(\log_{2}(4))$
By definition, $\log_{2}(4)=x$ means
$x$ is the exponent with which we raise ($2$) to obtain $4.$
$2^{2}=4 \Rightarrow \log_{2}(4)=2$
So,
$\log_{2}(\log_{2}(\log_{4}256))=$
$=\log_{2}(\log_{2}(4))$
$=\log_{2}(2)$
$=1$,
because $2^{1}=2$ (so $\log_{2}(2)=1)$
