If log_7(log_3(log_2x))=0, then x^-(1)/(2) equals

1983 AMC 12 Problem 12

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12.

\log_7(\log_3(\log_2x))=0,

then

x^{-\frac{1}{2}}

equals

\frac13

\frac1{2\sqrt3}

\frac1{3\sqrt3}

\frac1{\sqrt{42}}

none of these

Undo the logarithms one at a time, starting from the outside

\log_7u=0

implies

u=1,

then continue inward

The equation gives

\log_3(\log_2x)=1,

\log_2x=3

and

x=8.

Hence

x^{-\frac{1}{2}}=\frac{1}{\sqrt8}=\frac{1}{2\sqrt2},

which is not among choices A–D.

Therefore, the correct answer is E.